What are inclusive preferences?

What you prefer, including things like "but I want them to get what they want too!"

And is that the definition we have given the word "rational" here? Because I know for a fact that there are a few other definitions out there, for "rational" and for "rationalism".

Basically, yes. If you are talking about making rational decisions it means making a decision that best achieves the assumed goal. It doesn't mean making a decision that conforms to any set of cultural norms.

Anyway, if the little I understood of Timeless Decision Theory is right, isn't "a rule that everyone would like everyone else to follow" rational?

No, not at all. There does happen to be a small set of problems in which TDT agents will cooperate with each other while cruder agents will not but that cooperation gets no special privilege. It does whatever is going to win.