I don't think they are rivals, but they sit atop relative national systems where a lot of the people in those systems see the other as rivals.

I think these two leaders simply dedicate themselves to the best future of their country, and that means not putting their country second when dealing with the other. But both actually want mutual cooperation that benefits both of their countries, rather than one country 'beating' the other.

That's the Golden Age Trump is steering the US towards.