western is a cultural term derived from a geographic one. The US is also not 'western' strictly geographically as it is not in western europe, neither is australia. But they both originated from Britain's empire and share in it's cultural ancestry. It means "western europe and it's cultural derivatives". Spain and Portugal's empire fell away long before britain and france's and they don't have similar geopolitical relations like NATO, so it's hard to consider their former colonies/upstarts part of the same sphere of cultural influence.

China for sure will catch up, the question is what they will do with it. They're not ambitious like the US/West. The US wanted influence all over the world as an extension of the cold war and to keep economic interests safeguarded. But China just doesn't operate that way. They're more hands-off. They could be opening up alibaba cloud datacenters all over the US, offering it as an AWS/Azure alternative, funding tons of startups all over europe, the US,etc... to exert their influence, but they won't. They have a more long-term low-and-slow approach to global domination. The "100 year marathon" as they called it, which they'll win for sure.

China's greatest weakness is not just their lack of ambition,but their command-economy. They're doing capitalism but with central control of the economy. It intertwines government policy with corporate policy, making it harder to do business overseas (like with bytedance/tiktok).