Apparently I'm the first to rate this game, so... 

Great game, quite fun as it is, although I think the idea has a lot of untapped potential that could be unleashed with just some minor tweaking. Here are some ideas I thought of that could make your main mechanic even more fun to play:

1. Show the player what the next tile is i.e. is it a corner tile or straight tile, what rotation it is. This allows the player to plan further ahead. 

2. Add more tile varieties e.g. T-junction, four-way junction, and 2 straight lines that don't cross etc..

3. Remove the 5-turn cooldown on the request button; I know you put it there to place restrictions on the player, but I feel it is better to place restrictions on rotating/swapping the blocks rather than the request function. I suggest you experiment and play around to see what kind of restrictions produce more fun and strategic gameplay.

4. Have multiple blocks come down at a time. Not necessarily tetrominoes as they would probably be too big, but you could try dominoes or triminoes to see what it would add to the gameplay.

5. With that, should come the option to shift/rotate the block as it comes down, which would require a rethinking of the turn-based system. I suggest instead of having the block come down at once, have it come down one step at a time, so you have time to shift/rotate it as necessary. That new type of turn can also be used to rotate/swap your existing blocks, albeit with new restrictions put in as necessary.

6. Add some way to change the positions of the 2 endpoints of the circuit. Maybe make the blocks fall on top of them as well, maybe make them swappable (but only within their column), or maybe just generate new endpoints each time a circuit is formed.  Maybe even let them rotate as well. (Actually, now that I think of it, they don't even have to be in the leftmost and rightmost columns each time. You could even have them fall like the normal blocks each time a circuit is connected, in random columns each time in a random rotation, to keep gameplay interesting.)

My advice for you is really to experiment and play around with the main mechanic, and see what modifications would produce more fun gameplay. I've come up with a lot of ideas above, and I'm sure you can come up with even more yourself. I'm not lying when I say this game has a lot of untapped potential; I'm sure after enough playtesting you will have an extremely fun and perhaps addictive game mechanic. Add some graphic improvements and sound effects (yes, please add sound! A little sound can go a long way.), and some polish (e.g. swap animations), and you will have the recipe for a successful game on your hands.

I wish you the best of luck on your game.