Works perfect with Wine, just install in a clean wineprefix and use winetricks to install xna40.

All in all you'd be better off running it *natively. The port is available from the outlets that support all platforms, e.g. Desura, Humble Store and Steam.

Since I only learned about Escape Goat via a GOG "5 indie games for $5" deal, I can confirm that it Just Works™ if you install xna40 in a 32-bit Wine 1.7.10 prefix.

The simplest way would probably be to use the PlayOnLinux "Install a non-listed program" wizard since it's like a GUI superset of winetricks.

Also, I should point out that it's offered via a Humble Widget, so it won't show up on the Humble Store. You have to go to the game's website to buy it that way.

(I honestly don't get those widgets. I've bought many games that I first discovered in Humble Store listings but I think FTL is the only game I've ever bought using the widgets and only because I discovered it on GOG and then went looking for a Linux release.)

$ wine --version
wine-1.7.15

(sorry for the slow answer, but if you do not quote there is no notification)