not only competition but compliance. The legal obligations a car manufacturer has to satisfy in the EU nowadays is wild, IUPR, OBFCM, WLTP are just the programs regarding emission checks. There are many many more.
The big Chinese car companies are managing to build compliant vehicles now. BYD, SAIC, Great Wall and Geely all sell vehicles into the EU market. It's hard, but it's not like the barrier to entry is so high these companies can't meet it.
While their entry level car (Atto) is the same price as the cheapest spec Tesla model 3. Their Tesla model S and X equivalents (Han and Tang, respectively) start at almost half the price of the respective Teslas.
On the whole BYD don't seem to be wanting to compete at the bottom end of the market and are pricing their cars around the same level of their 'competitors'. They don't want to offer the cheapest electric SUV or even best the 'cheap' SUV, they want to offer best $80k electric SUV.
That suggests they aren't really competitors though, so either Tesla will have to drop to the point where they won't be profitable any more or there are substantial quality differences. BYD's vertical integration may become the differentiating factor if they can get the public to trust the brand.
Based on their marketing and pricing it seems their base pitch is "get a $100+k 'worth' of electric SUV for $80k". So they're competitors in the sense that they're targeting people who just about have Teslas Model X or BMW iX money, but would still like a bargain.