> So checkmate in any one timeline counts?

Yes. ( https://news.ycombinator.com/item?id=24065059 )

> You couldn’t do all timelines.

How do you reckon that? I mean, it makes sense on an intuitive level; however, since now we're not talking about Conor Petersen's 5D chess, but the vast space of possible multiverse time travel chess variants, it's not obvious how one could prove this to be impossible in a somewhat rigorous way. For example, what if time-lines end when a king is mated (or wioll fore-when haven been mote [0]), but you only lose when you can't make a valid move in any time-line?

[0] http://pages.cs.wisc.edu/~param/quotes/guide.html

I suppose you would have to avoid the king escaping to another timeline?

You do , which is why it ends up being easier to attack kings in the past. Because you can't change the past, only create new timelines, attacking a king from any previous board state means that the attacking piece must be captured.

does this means that attacking the starting king position will always put the king in check of the very first board? but, he can't really escape that

Yes, but it's not that easy. Pieces still make threats according to their movement rules, whether through time or space.

For example, if your king moves from its square and an enemy rook attacks its starting position (rooks can move any number of squares in any one direction), then it's mate unless you can take the rook. However, if in the intervening time, another piece lands on the same spot, then it will block subsequent rook checks through time on that square.