Well, I see where Amanita Design said the game's native resolution is 1920 x 1080, but that the "game works great on any screen resolution".
I decided to test this out a bit, so I changed my display resolution to 1024 x 768 and then 800 x 600 to see how that worked with the game. One of the nice things about the game is that you can "grab" the screen and pan around by clicking the mouse, holding the button down, and then dragging, so you'll be able to see the entire screen that way.
Only tricky part for you might be when exiting one screen to get to another one, as it requires clicking the mouse after your cursor has morphed into a little white arrow, which it will only do when it's close enough to the edge of the screen, like this:
http://f.cl.ly/items/2i3V1J3b223u0L23191L/gnome.movSo while playing for a few minutes, I could see enough of the arrow with the 1024 width to exit a screen either left or right, and enough of the arrow with the 600 height when exiting a screen up or down, but eventually I noticed that on a few screens I wasn't able to leave the screen either to the left or to the right (when at 1024 x 768) because I couldn't get over far enough for the white arrow to show up. However, you can use the mouse scroll wheel (or tap the spacebar, or use the up and down arrow keys) to zoom in, and zooming in when near the edge of a screen made it so that I was then able to see enough of the arrow to be able to click and exit the screen. If that's confusing, I've posted a couple of screenshots to show how zooming in gets you closer to the edge. Shots before and after zooming:
Also, If you would like a more definitive answer from the developers themselves, you can contact them by using the form at the bottom of this page:
http://amanita-design.net/contact.html