China's internal EV market is enormous, and by any reasonable metric Chinese manufacturers are already "winning that race". Several major cities have fully electrified their bus and taxi fleets for example, and most of those vehicles are made by BYD Auto, which was delivering more cars per year in 2012 than Tesla does now. But there's plenty of EV market to go around, both in China and elsewhere. BYD doesn't currently ship private cars outside China, only taxis and commercial vehicles like vans, buses, delivery vehicles, utility service vehicles, but this can change rapidly. The main reason this isn't currently happening is that they don't want to deal with consumer support outside their core market, and are more comfortable with institutional customers. However, I don't see it as a race. The main thing holding back EVs in both the Chinese and non-Chinese markets is infrastructure and obstructionism by fossil interests. I see that changing quicker in China than in the West (but I still have hope) so it's more likely Chinese EV manufacturers will expand more in China than internationally, until they see a more valuable market. Tesla is much more aggressively expanding in the West, and building out their own infrastructure to do so, and are the primary focus of the hate by western fossil interests.
If and when the landscape on the western markets changes to be regulatorily more favorable and provide sufficient charging infrastructure, I fully expect Chinese manufacturers to entirely own the lower half of that market, because even the cheapest Tesla can produce is way way more expensive than your average petrol car, whereas Chinese-made EVs are competitive with petrol on the Chinese market already now, and prices keep dropping. A new BYD e2 with extended (253 mile) battery sells for the equivalent of $25k. The Tesla model 3 sells for twice that on the same market. On the lower end, with smaller batteries, you have cars like the Levdeo i3 with 100 mile range which sells for the equivalent of $10k, and the phenomenally cute Wuling Hongguang Mini EV (75 mile range) which sells for the equivalent of $5k. Tesla still owns the luxury EV market everywhere, including in China, but there's simply nothing they offer in those price ranges, and that's where the big volumes are going to be in the future as infrastructure catches up. Still, because luxury cars have higher profit margins, I can see Tesla surviving and holding a large part of that segment.
There's also a huge market for EVs in the global South, where infrastructure is currently abysmal but there is extreme sensitivity to fuel prices. The market there can move very rapidly in response to even minor infrastructure improvements, and small cheap EVs would be the primary seller in those markets. Tesla has no chance there, but the Chinese EV vendors do.
If there's anyone losing the "race" it's traditional Western and Japanese car vendors. They fucked up time after time, and are the tail-end of the current EV industry. I don't see a path where they get their shit together fast enough to not be overrun by Tesla and a bunch of Chinese EV vendors, so they can only win by creating regulatory roadblocks.