I'm running WINE on Linux Mint.
Functionality is reasonable but not 100% reliable. I managed to get all the way through Mass Effect 1 without any issues at all, ditto Grand Ages Rome and Men of War.
Thus far I have been able to get the following games to install and work.
Mass Effect 1
Mass Effect 2 (crashes on some visual fx, though that might be my pc not WINE)
GTA Vice City
GTA San Andreas
Grand Ages Rome: Gold
Brothers In Arms - Earned in Blood
Portal 1 & 2
Men of War: Assault Squad
Men of War: Red Tide
Various Call of Duties
Civilisation 3 & 4
Rome: Total War - the campaign part works and battles can be resolved automatically but the game crashes when you try to manually resolve battles.
Sins of a Solar Empire
There are issues: performance is below Windows on the same box, audio can crash - requiring a restart sometimes. Some games can be backed up by having their folders burned to disc and can be "installed" merely by copying the folder back (GTA:VC and Unreal Tournament to name 2). Many games get quite upset over this and seem to require an actual install.
Be warned - some games use absurd DRM systems that mean that if you go through a period of multiple installs, due to technical difficulties, you're likely to get a "you have exceeded the maximum number of installs, please contact..." messages. Utterly hateful. I have 2 games that this has happened to - both are games I bought legit copies of after discovering them via torrent sites.
And they wonder why people steal.
It's so sweet not to have to reboot to play and WINE has come on hugely over the last few years, but, as much as it pains me to say it, for a dedicated gaming platform you'd likely be better off installing Windows and then stripping out all the unnecessary services and crud.
For the record, I've tried the same setup on Manjaro - many mouse and keyboard issues under WINE. On Slackware I've had mixed success. Sometimes, installing Slackware, plus extras (you have to convert Slackware64 to multilib yourself to get WINE to install and run) leads to a perfectly working WINE and games. Other times, installing from the same media, using the same method seems to lead to WINE refusing to work on anything. I'm simply not technical enough to be able to know how to circumvent such oddities.
Hope that helps.