Seems like I’m always rushing off, but there are a few things I have to say before I go. First off, if you notice in the splash page to this great game, our hero, Sneaky, is holding the screwdriver, maybe that’s a hint. It is hard to find even when you know which room it’s hiding in. I’ll put the spoiler in the alt text.
Second thing, the unusual map is called World Inversed (his word, not mine), and is by an artist named Vlad Gerasimov. All the information you need can be found at this site.
Now without further ado, here is the map: