Well, turns out one of our computer ".godot" folder got all messed up which causes all this weird issues only when exporting in web... We still have issue on our game depending on the browser (Opera and IE for example) and some weird graphical glitches on Linux...
But the nice thing with Godot is that it is becoming better and better with time, and way more stable :)
Sure, we will be glad if you try our game ! You can find it Here. We are especially open to honest feedback since it's our first time making that kind of game.