Per capita emissions are relevant in the sense that if China broke into ten separate countries tomorrow, with each new country maintaining their current level of emissions, the effect on the planet would be the same even though an entity called “China” is no longer at the top of the leaderboard.

There is some per capita carbon emissions budget such that if each human on earth stayed within that budget, climate change could be mitigated[0]. The average Chinese person exceeds that budget, but does so by significantly less than the average American. So the average American is more at fault for climate change than the average Chinese person is.

Of course, your second claim, that this is a global issue, is correct. But if we solved the global issue in a fair way, China would still emit a few times more CO2 than the US.

0: “Mitigated” rather than totally solved, because to go back to pre-industrial temperatures the budget would have to be negative. But let’s say we’re talking about staying within 2C or some similar goal.