Why should we care about that? Even if you wanted to argue our individual fates are tied to our country's, we don't all live in the same country, so how, actually, could we all care? Are you really convinced its so zero sum like this?
We collectively spend decades and decades creating a sophisticated global capitalism, huge networks and infrastructures of trade and travel, just to find ourselves in some dark forest-esque race with everyone else anyway? Is this really consistent to you? What was the point of anything in the last, like 40 years to you if we just need to act like we are still in a cold war, except this time its a war with everyone?
"Other countries" means China here, I think. China got a little on board with the global capitalism (and lifted 800 million people out of extreme poverty along the way, if we're looking for the point), but never really embraced Liberalism and so ideally isn't the one aligning superintelligence. It would be lousy if Russia or North Korea or Somalia was in that position and it would be fine if the UK or Denmark or Brazil or Ghana was, but none of that matters because none of them will be in that position. Only the US and China are playing the game.
We're you around for the space race?
It's a world prestige thing, and also a competitive edge, for better or worse.