Let's see, I would put a few pieces on the board, give up, and then we would commence play...
If time ran backwards, how would you experience your chess games?
Then we would always come to that one position where all the pieces are on the board, realize that it's way too complicated for anybody to figure out, then put the pieces back in the box and go start--or end--something else.
If the "arrow of time" could point in either direction, the laws of thermodynamics wouldn't "work".
Laws of Thermodynamics... Oh that's precious... And who exactly wrote those laws? Some scientists.... And what's more, they didn't even experimentally derive those "laws" but rather declared them _on_principle_, because they kinda fit with our understanding of the Universe, at the time... Wait about 100 years and everyone will be laughing at your "laws of thermodynamics" the same way people are laughing at the Newton's laws today.
This statement reveals the definition of time as we know it.
If the "arrow of time" could point in either direction, the laws of thermodynamics wouldn't "work".
Laws of Thermodynamics... Oh that's precious... And who exactly wrote those laws? Some scientists.... And what's more, they didn't even experimentally derive those "laws" but rather declared them _on_principle_, because they kinda fit with our understanding of the Universe, at the time... Wait about 100 years and everyone will be laughing at your "laws of thermodynamics" the same way people are laughing at the Newton's laws today.
You mean I worked all those problems for nothing!

The notion of "time running backward" is rather an intuitive one, because we obviously cannot experience it. But if you subscribe to the basic notions of physics, then you have to accept that there's nothing special obout our "arrow of time" and that this arrow could equally well point in the opposite direction....