Certainly not for property taxes.
If a major tenant vacates an office building (for example) in Manhattan, the landlord will simply sign another tenant to take its place. The assessed value of the property may rise or fall depending on the lease terms, of course.
For a sports venue like Madison Square Garden, the value of the property is directly linked to the presence of the major sports teams that put the venue on the map in the first place. MSG simply wouldn't exist without the Rangers and Knicks. This is probably a major reason why -- unlike the typical example of a major office tenant -- the building and sports teams have the same owner.
I'd also point out that assessing property taxes on a sports venue like MSG would put New York City at a competitive disadvantage against jurisdictions that don't. Most professional sports teams play in venues that are owned by public or quasi-public authorities and do not pay property taxes. The Meadowlands Sports Complex in New Jersey, for example, was originally built by the New Jersey Sports & Exposition Authority. The agency still owns the land where the stadium is located. The two teams that own the stadium jointly -- the Giants and Jets -- pay no property taxes. The same is true for the Prudential Center in Newark, home of the NHL's New Jersey Devils. Even the Barclays Center right in New York City in neighboring Brooklyn is exempt from property taxes under a deal somewhat similar to what MSG has in Manhattan.
Well then, tax only those businesses who gain from it; hotels, restaurants, parking garages, marketing firms, etc. Don't tax an entity that not only doesn't gain anything from the venue, actually loses out because it interferes with their business that the city is already taxing.