If you are unique, and keep browsing with the same set of parameters, then they can track you (any web, not just YouTube).
Private tabs tweak some of those parameters to make you appear less unique, so webs have a lower confidence in you being the same person, are less likely to correlate that tab with your actual browsing habits, and less likely to punish you for “past transgressions” like having used an ad blocker.
Private tabs also clear up any data stored in your browser by a given website when you close them (not just cookies or site data, but also whether it has some fonts or tracking pixels in its cache), usually have fewer extensions enabled (each extension and data stored in it can make you more unique), and so on.