OK after some fiddling about I found out that to place towers you have to hover your mouse over the square and hit ENTER. Works fine, however its not ideal if you ask my opinion.
The game seems to be very buggy when moving around with the AWSD or the Arrow keys. If you hover over any square that can be interacted with, be it a green tower square, a unit on the move or anything else, moving the arrow keys will bring up the menu for that square as if you had hit ENTER, which means you have to either use edge scrolling or move the mouse away from any squares to stop it from happening.
I love the concept and twist of a genre I love, and it seems to be designed well enough for a budget title and it needs a lot of attention from the developers, but so far after the first few single player missions, it shows some promise.