Not sure if it is related, but aside from the kernel, have you tried newer Mesa? If you want to try something like this, be sure to have a backup. Last time I tried updating mesa stuff on Mint, the system basically collapsed on me (removed Cinnamon and couldn't get it back).

Busy upgrading now to Mint 18.1 which has a newer version of mesa. And it looks like Intel offers upgrade stacks over here https://01.org/linuxgraphics/downloads which is only available on the newer Ubuntu distros. 14.04 is not supported anymore.

Don't care about that. That's the same as an updated mesa, basically. So you don't need it.
If you are doing an upgrade, check things in the end, as Mint upgrades tend to only upgrade Cinnamon and co, but not kernel and mesa. They have some weird ideas and eventually made me go back to Ubuntu (the Mate version).

Okay well I installed Mint 18.1 and it came with a newer version of mesa, 11.2.2.

And now CS seems to be working just fine, albeit with 30fps lower than Windows 10 :(

I tried using that Intel graphics installer (and faking the lsb_release to trick the installer in to thinking it was running in Ubuntu 16.04 and not Mint 18.1), and it did indeed update/install quite a few packages but nothing groundbreaking by the looks of it.

If you have any other suggestions to make CS run smoother (only getting about 50fps at the moment), I'll gladly give them a try.

But anyways, thanks! At least it looks pretty now :D

Some time ago I read something about CS, but I am not sure. Maybe try to change its settings, like v-sync. You might find more tips in its steam discussions, there should be a thread about it and Linux performance too.