The blood-soaked neon-fuelled slasher Akane [Official Site] released with Linux support, I took a look to see of it's worth your pennies. Note: Personal purchase.
They did have a bit of a launch mess-up when it came to the Linux version, where it resulted in an empty download. I messaged them how to fix it and they managed to get it going quickly enough.
The idea is simple, you're trying to kill as many yakuza as possible while darting around a small area of 2121 A.D's Mega-Tokyo. There's a lot to appreciate about it in such a small package, from the excellent style to the fast-paced addictive combat and it runs perfectly on Linux.
It can be quite difficult too, you need some fast reflexes as well as some seriously good hand-eye coordination as one hit and it's all over. I can't honestly count the amount of times I've been taken down now, always people with a gun too, I just can't react fast enough. Like all games though, you do slowly get better at it and it's so slick that it makes me want to continue playing more. Some of the moves you can pull off are awesome too, the adrenaline mode is fantastic as you quickly slice through a ton of enemies all at once.
There's currently no official gamepad support, so get your mouse ready for some action. The developer did say they're planning to add gamepad support, as well as keyboard input customisation in a future update.
Check it out on Steam. It's 25% off until September 17th. Even without a discount, it's pretty cheap at £2.89.