What if Chess never existed?
Someone would have invented something similar. The norsemen had a game called tafl (from memory) which looked similar in some respects.
There are a number of other games that have chess-level participation today: checkers and backgammon are two examples. There are, of course, other ancient games that could have been developed into something like chess. In the Cairo Museum and when the King Tut Exhibit was in Washington, D.C., I remember seeing a 3000 year old peg and board game that resembled a cribbage board though I don't think it was just for scorekeeping.