Excellent Game. Nice and Simple graphics and a good way to test circuits. Reminded me of the "Digital Logic Design" course i had taken in undergrad.
I think the circuit joining part is working perfectly, but what if we want to remove a point from the circuit, that we think does not solve that. Perhaps we could have a way remove a point from the current circuit lets say by right mouse clicking that point. You can also add a overview like a minimap to show the current look of the overall circuit. Overall the concept is working and you should update this after the game jam, as it has a lot of potential and not many people attempt this sort of stuff.
Keep up the good work :)