Max Payne 3?
Sounds a bit like that scene where your boss' children are kidnapped.

Yes!

Boss has no children though. It's his wife (though she could be his daughter...).

Might be, might well be; it's been a while since I played the game so small wonder I don't remember it that well. Should Rockstar remove their additional DRM, I guess I will have to play it some more.

Anyway, here's the next game:

Great, just great! The place has just been blown to smithereens, we barely escaped with our lives! And just look at what a ragtag team we have: a kid, a walking fur carpet, an ex-soldier who can't get over his past, a common cutthroat and an upstrung war hero. And me, naturally. But that is the thing: I don't remember much about my own past. I mean, obviously I have one, I just... it's kind of blurry. No matter. Now we're headed for the temple, to report what's happened and let others sort things out.

That sounds rather familiar! Can you describe the setting a bit more? Is there magic in the game?

The setting is a rather well-known one so I'm somewhat at a loss about how to describe it so it's not a dead giveaway. Let's say it's rather sci-fi, with aliens, robots and lasers.
Nah, no magic in the traditional sense. There is, however, certain power that allows one to do things that people normally can't. That arrogant war hero can use it, for example, though for some reason "chose" not to, so we had to enter (and win) an illegal racing contest to break this overconfident knight from slavers. And did we get any thanks for that? Yea-a-a... no.

No idea what game but sounds like something I would want to play.

Huh, I haven't played that many scifi games. This sounds totally cool! Is it from the Star Wars universe? Actually, this sounds more like Mass Effect which I haven't played. ME2?

Yeeeeees. :-)

Huh, I don't remember an adventure with a kid and Wookie - that's what the walking fur carpet is, right? ;)

I've only played bits of both KOTOR, so I'm gonna guess it might be the first one?

Indeed it is.

The "kid" is Mission Vao. Yeah, she's not a real kid, but she's being called that often enough. The wookiee is Zaalbar, naturally, the war hero is Bastila Shan and the rest are Carth Onasi, Canderous Ordo and the player character.
The event I described was the aftermath of the bombing of Taris.

Here's my go: I'm a pirate captain and I have a totally awesome airship! And now it's time to go flying around the world with my crew, having adventures and saving the world (as usual). :D

And it gets even better. :-)
The characters are quite vivid, each of your companions has a side quest that you'll get a chance to complete. Just try not to miss it. Say, it might be a good idea to include a wookie in your team while you're on Kashyyk or let a certain wisecracking Grey Jedi tag along while you're on Manaan. :-)
It's yet another MMO game, isn't it? :-)

//Somewhat unrelated since the game's not out yet, and thus cannot be the one that is up, but this might fit the description.
//And yet another unrelated remark, the first thing that came to my mind when I read about pirates and airships. :-)

First thing that came to my mind:
https://www.youtube.com/watch?feature=player_detailpage&v=8YxXc4DDHpM#t=14

I saw that as a kid!! I love it! What's the name of the cartoon? Can you google it in your language and then cross-search on Wiki if you don't know? By the way, is that Arabic, or Persian, or Turkish? Or some other language?

Thanks for bringing that up! :)
It's not an MMO game. It's a single-player game. :)

Also that looks great, I feel like I've heard about it before - do they have anything in common with the people who made the sea exploration game based on that web game?

Treasure Planet is one of my most favourite movies!

A hint: You're a pirate captain.