Neat idea. Cross can win every time in 3 moves by playing between the 2 boards. As long as they get 2 in a row they will win. It may need a way to mitigate that. Great work. 

I actually also have this idea of "TictacToe with multiverse" but i scrapped it because when i tested it on paper it has so much problem that makes the game unfair. my idea is quite different though actually

And it's looks like you didn't test the idea on paper,  in this game obviously the 1st player could always win xd

I quite like the idea. I took some time before noticing that you can move between grids.

The problem is that you can always play on the first empty grid. The game cannot end if both players play this way. I can't think of a mechanic that would fix this problem, but I think limiting what grid are available to go back can create interesting situations.

The game is quite polished, well done!