I have a similar issue. I am typing and all of a sudden I've offered a rematch. I think after the game, the behavior of the program is to make the buttons next to the board the "current buttons" (or whatever the right language is). The space bar is a button press of the current button. So while I'm typing "good game" the space bar actually issues a rematch. Easy to abort the game, but annoying all the same.
Backspace button
Yes, it seems the program forces .focus() on a button or something, that enables my browser to respond to backspace as go-back or space as 'rematch'.
The .focus() should ALWAYS be on the text box, after a game, because it is customary to say gg, in all games on the internet. If I want to rematch someone, or go back in my browser, I'll click the button.
So most browsers have this feature where if you have no text box selected, and you press the backspace button, then it takes you back a page.
This has become quite an annoyance in live chess. You finish a game, and then you type something like gg to your opponent, and then your opponent says something, and you want to respond, and maybe you make a spelling mistake, but somehow when you press backspace, oh, it just took you right out of live chess.
I'm sure you have noticed this if you chat at all in live chess games. It's not really the browsers fault, because in normal situations, like forums and stuff, I never have this problem where I press backspace and it takes me back a page, because I'm always in a text box when I press backspace.
Yet somehow, live chess forces me to lose focus and backspace a spelling error and there it goes! It's definitely a software bug (although very minor bug).