Welcome to the forum.
The function of the centre button is assignable, so you should check that it hasn't been set to do something else.
If it's the same operation as the RX100 mk1, press Menu > Cog symbol > Page 2 and then you should see "Func of Center Button". This should be set to "Standard" so that it works as you expect.
After that, check that you aren't in some shooting mode where focus tracking isn't supported. The full manual (online) explains the permissible combinations.
-R