Game suggestion for 2 players

If you are looking for only 2 people, A way out is a great choice :D (origin only tho)

Or maybe Stick Fight: The game? It is a good stress reliever.

Borderlands 2 while not short, it is absolutely not the grindfest some people claim it to be, at least surely not for the first 2 playthrough. 3rd starts getting seriously punishing. Basically you can play it without any extra farming and backtracing, you don't need special weapons (and also any build works on first play.)

Magicka 1, 2 or maybe Helldivers. Magicka 1 and 2 has story with pretty short levels, fun gameplay, good to mess around with. 1st is a bit more crude, balance is worse as you mostly can destroy everything with 2 spells during the whole game.
2nd's gameplay got more mobile - you can move while casting, or even kite around, and the game shifted the focus to resistances and weaknesses a lot,very clearly inspired by the arena-PVP Magicka game. I think it would suit you two really well, it's similar to MOBAs in a way that you have a special spell rotation of your choice, you can use any effects as you want with the typing, and positioning and Crowd Control got a lot more important. Should be a very easy change after DOTA2.
I played only a bit with Helldivers, but it felt like spaceship troopers meets a hard military setting where communication and teamwork is essential, and specials are used by typing, similarly to Magicka (but maybe with arrows? not sure). Sync your reloads, tell others when the ammo drop comes that you ordered and where before it crashes them, use granades and other specials while going on individual maps for a mission from a HQ hub. Not sure if this has a story mode other than the missions, but the separate missions format would fit your time requirements, while the game requires and rewards teamwork and cooperation. (I'm still waiting for a nice sale, this felt like one of the rare coop games where it's not coop as "we play on the same map together lol" but coop in way that you need active cooperation.

FORCED (Slightly better edition) has short arena maps where you play with your pick from the 4 different gladiators, having a special energy ball suspended between them, and you use the ball to manifest special effects (heal, damage, explode, you can call it or push it away from you to manipulate it) while fighting off enemies, destroying spawns and killing a boss. Takes < 10min .You unlock weapons, perks as you achieve goals (3 different from each arena) and you need very, VERY active cooperation to complete more than half of those objectives. Like you move down, call the orb, destroy spawner, while your teammate kills the new enemies in the top right to get to the next position to call the orb as soon as it is possible to beat a time challenge.
TLDR: brawler gameplay, with unlocks that require thought out strategy and cooperation to get some objectives, that rewards you with pretty hefty unlocks. You know, that kind of a game that makes you murder everything on a level, then you need to think a bit for a challenge and complete it, then use the unlock to do more special challenges, and as you get more accustomed, it starts pushing your ability, and knowledge of the game, coupled with your unlocks to solve further objectives. TBH this game feels the most serious from the you have to plan, and work together aspect.

Ibb and Obb, which is a coop, depend on eachother to do puzzles/jump platformer.

Broforce!
And Trine games

Maybe Rocket League? 5 minutes per match.
Thanks for the giveaway!

GANG BEASTS!

Saints Row 3
Saints Row 4
Borderlands
Left 4 Dead
Left 4 Dead 2
Barony
Team Fortress 2
Dead Island
Worms
Mortal Kombat/Injustice [It's the same for me]

This is the ones I play with my friends/wife

Some Coop Puzzle game if you like

• we were here (free)
• we were here too
• tick tock a tale for two

three short game but very nice if you like puzzle

one hour session you can play rocket league if you like, pubg maybe..
trine? never play but seems great

I hope you find your happiness with me or someone else

You could try some mmo survival games, like Rust, Savage Lands, or what I'm into recently - Citadel: Forged with Fire. But that being said, I haven't playe 1st two, and last one is actually quite grindy.
You could also try twin stick shooters like Tower 57.

Currently playing Armello on and off with my own friends - Although it's better with 4 players. Can add AI players to make up 4.
Any of the Civilisation games
Age of Wonders
Anno
Dungeon Defenders.
Terraria

Online Board games like Evolution, Carcassonne etc can be fun too, just as something very quick and casual to play with a friend.