Steam on Windows 7 64-bit, on VMWare Workstation player, running on Linux Mint 18, with NVIDIA Drivers v370.28. Also latest version of VMWare Tools.
What happens: I start SKSE. It doesn't recognize my 3D graphics "card". Given the 3D graphics "card" is VMWare's SVGA 3D emulation, that's entirely expected. I tell it "Medium" as a good starting preset. I click "Play", it starts up, shows the Bethesda gear logo, plays a second or two of audio clip (staticy and distorted), then the main menu screen shows up, with no background. The mouse leaves a trail composed of copies of itself, I click on "Mods" because I've done the default cart-ride and I want to make sure Alternate Start is turned on. It freezes. This happens in fullscreen, fullwindow, and borderless fullwindow.
Alt-tab, ctrl-alt-delete, both work. I close Skyrim by right-clicking on the icon on Linux Mint's *bottom bar.
I come on here to complain bitterly that my free game isn't working on my specialized, niche platform in a market composed of a few dozen different things composed of a few dozen different variants on those things, created to standards almost no-one follows completely and exactly, except possibly now and then, and which standards literally cannot always be followed completely and exactly without a complete redesign of $Vendor's platform.
Anyway, if there's any more info you want, I can probably get it for you.
* Or top, left, or right, I suppose, depending on which style you like.