Party Hard

Absolutely. I have some friends coming over this weekend and we are playing Drawful 2 actually. Epic also gave away Jackbox Party Pack 1.

BTW, you don't need a controller to play those: players use their own smartphone / tablet to answer/draw/control.

I should preface these recommendations with a disclaimer: I've only personally played a handful of these with/against another person, and all but one of those were many years ago. (And two of the three I'm sure about were only played multiplayer in split-screen on a console.)
Nevertheless, I've played all the games by myself to enough of an extent to recommend them (at least conditionally) on that basis, and I've watched multiplayer videos online for a few of the topmost titles.

In roughly the order I would recommend them, with some stream-of-conciousness thoughts about each:

Terraria -- IP-based multi, IIRC; Everyone could play at once (no idea on the upper limit), and it's co-op by default (anyone who wants to participate in PvP has to opt in during gameplay); very much a "wiki game" (i.e., having no tutorial was treated as a feature, not a deficiency), so if no one in the group has played it before, a lot of the convenience features of the interface will have to be discovered or looked up; open-ended sandbox, with enough different things to do that everyone might find something to engross them (or at least keep them busy

Talisman: Digital Edition -- Supports up to 6 players, either on the same PC or online; rather cutthroat (though this can vary, depending on your players); lots of RNG; turn-based (though turns are typically not very long); a single game can potentially take a few hours (though there are setup options to mitigate this somewhat); for online play, only one player needs to own a given expansion for that to be used in the game being set up; there's also usually one expansion available to try for free from the new game setup at any given time (though the base game is fine by itself, and preferable if no one's played before)

Death Road to Canada -- 4-player same-PC co-op; very goofy, despite the zombie apocalypse setting and scavenging-focused survival gameplay; run-based RPM (a.k.a. "roguelite")

Streets of Rogue -- 4-player co-op (I think same-PC and online?); another run-based RPM (mission-based); arguably less zany than Death Road, but still very light and humorous; tons of options to tailor the game to your tastes (within reason ;P )

Oh...Sir!!! The Insult Simulator -- 2-player head-to-head only (same-PC or online, though); turn-based; an individual match will take less than 15 minutes (I haven't timed it, but I'd guess less than 10); very silly humo(u)r "inspired by" Monty Python (and so requires at least a tolerance for that); might serve as a good palate cleanser between other games/activities

Spelunky -- Has same-PC shared-screen co-op (the normal Adventure mode) and competitive (Deathmatch); even if you find Adventure mode more frustrating than funny, Deathmatch can be great fun (though perhaps only as a palate cleanser between other things)

Barony -- Supports online or LAN co-op for up to 4 players; another run-based RPM (though it's the only one on this list that I could understand someone calling a "rogue-like", since Barony's a dungeon crawler heavily inspired by NetHack); first-person & real-time; you can turn off or change some of the nastier mechanics via the options if you find the game too lethal (though it'll still be difficult)

Caveblazers -- I think it's just 2-player same-PC co-op (with dynamic shared/split screen); gameplay's like if Spelunky were focused on combat, with a side of running up, jumping off of and sliding down walls (unfortunately, neither the fighting nor the platforming/traversal are helped by the somewhat indistinct and thoroughly unimpressive pixel graphics)

JYDGE -- Same-PC co-op only (not sure if it supports more than 2 players); a somewhat nonlinear mission-based twin-stick shooter; the only 10tons game I've played -- some others are probably better for sheer jump-in-and-kill-stuff carnage, and might support more players as well

Unreal Tournament -- LAN or online supported (no clue about the number of players, but, certainly, six won't be a problem for most maps & modes :P ); it's an arena FPS, so skill disparities will really show here

Quake III: Arena -- See what wrote for UT above: everything there applies here =P

Unreal -- Same deal as UT, but the multiplayer was a sideshow to the single-player campaign; UT was an iteration upon the multiplayer from this one, so if you were up for an older arena FPS, there would be little reason to go with this, unless you already had particular experience with/nostalgia for this one

Din's Curse -- An indie "Diablo [II]-clone" ARPG with IP-based MP & no official cap on players; kinda janky and old-looking, and there's zero story (only sparse tidbits of "lore", and the thinnest of excuses for why you're doing what you're doing); old enough and low-spec enough to run on just about anything, though, unlike Grim Dawn

Epic Pinball: The Complete Collection -- has same-PC multiplayer in only the loosest sense: players take turns playing solo rounds, with play passing to the next (IIRC) every time a ball is lost (probably not counting bonus balls earned through gameplay), with the closest thing to in-game interaction between players being comparing scores once the last ball of the last player's drained (giggity); I haven't played it on GOG (though it's in my library), but from what I remember of the couple tables I played years ago, it probably only supports up to 4 players in this way; might appeal to any oldsters in the group, but I guess the DOSBox-y nature of it might work against the interest of the younger family members

I was thinking about something along the lines of Quake or UT too, but considering the youngest player is 12, it might be a bit early. Personally I'd wait 2-3 years for that (my kids too, anyway, they're not yet interested), but of course every parent has to decide this on their own.
Also the OP mentioned the problem with CS was skill levels - depends if tactical or twitch skills are lacking. Simple deathmatch is probably easier to get the hang of, once the controls are mastered.

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Since the OP mentioned the problem with turn-based game is losing interest during other players' turns, maybe RTS games could do it? Would probably have to something coop oder team-based (so the less proficient player can have a strong team mate to compensate) like 2 vs 2, but since I don't play neither RTS nor MP I can't give any recommendations, don't know if games like that even exist.

I had a good laugh with my friends playing 'heave ho' where you have to work together to reach from point A to point B. Not sure if it has online multiplayer connect though. Another fun game is Ultimate Chicken Horse.

ARPGs are indeed fun to play with friends, I would think they keep kids at that age busy since you are constantly doing something but when I think about it the building of the character, skills and loot might be boring to them.

I am not exactly sure how the multiplayer works for "No Mans sky" but that one is pretty easy going and has base building aspects, I think you might have to go online around other players and also you might have to play a little while before you can go find the rest of the people you play with (Gate).

Then there is always Minecraft, kids just love that stuff.

Thank you for your detailed list!

Terraria, Starbound and other building/farming games would be great for big sessions, wich is not the case. Maybe we try Terraria eventually, being able to leave and join at any time is a big plus.

We have played a couple of session of Talisman on a tablet, while camping. but at the time I feel something with more action is needed to hook the kids.

Have played a bit of Streets of Rogue with a friend, it's definitely a fun game.

Fast paced FPS are not a problem for the kids, the adults are the problem :)
The 12yo play CS-GO, Valorant and such competitive, team based FPS all the time and is quite good at it. The father doesn't mind since he usually with the older brother.
Now that I think about it, Team Fortress might be option, due the various classes.
We tried Minecraft once but you know, Minecraft is so last century, look at those pixels! And it's for babies!

I actually like the game.

Only official servers. Europe or USA.

I admit I have not tried it myself, but I have younger relatives that have played it ALOT and still do sometimes, ages 8-17ish :)

Then they probably wouldn't like Barony, either, as it's also a first-person game with voxel graphics. :P


I also just though of another one: Towerfall: Ascension. I haven't played it at all, but I know it's got local-only multiplayer (co-op and competitive, though the latter seems to be the focus) for up to 4, and from what I've seen of other people playing it, it would be a blast.

Try out Fortified, a 3rd person Shooter and Tower Defence game.

Check out 'Keep Talking and Nobody Explodes', you might like it. And also, if you're into survival games, maybe 'Don't Starve Together'.