SB Recommends GNU/Linux Games
Linux gaming is in a realy nice spot at the moment. Support from Steam games is growing, and the popularity of game making tools like Unity 3D mean that there's a whole bunch of interesting shortform stuff availible for free.
Steam can be a little finicky depending on your distro (it favours living in its own little sandbox of drivers), but its popularity means there's very likely a way to get it running! It works great in Ubuntu, and Arch has a simple workaround (just add a prefix to the program's launcher) in their wiki.
And of course things like Wine (and it's derivitives), DOSBox (and other emulators) and virtual machines makes it pretty easy to run a whole bunch of things from other operating systems.
Intentionally Wrong: Playing this feels more like I'm trying to overcome myself than my opponents, since I've noticed I tend to win any match where I spend at least 5 minutes simulating before I send in my orders, and only lose if I get careless and don't take the time that I need. Perpetual vigilance and attention to detail is rewarded.
JoeX111: I love the asynchronous multiplayer. It's like chess by mail with gunfire.
Dracko: You should be playing Frozen Synapse anyhow if you've got nothing better to do than completely miss the grotesque irony of a cyberpunk tale about violent corporate warfare using proxy soldiers.
Ymer: I think you might like it actually. It's XCOM
style turn-based combat only both players turns take place at the same time after they've been planned and engaged. You can even simulate whatever move you think your opponent might make during the planning phase but you're of course in all likelihood gonna guess completely wrong about it. The multiplayer is also asynchronous similar to Words with friends/Wordfeud so you can have multiple games going at once and not have to make your move in any of them for days if you so wish.
Also a campaign with a real weird GitS-like storyline or something.
The Blueberry Hill: Tight, turn-based tactical game. Really great as a play-it-when-you're ready asynchronous multi thing, with lots of options for your you people, and for simulating the behaviours of your opponents'.