No, but Mauser set the standard for all bolt action rifles that came afterwards when he introduced his iconic rifle that would be designated Gewehr 98 or G98. Rifle makers started to use some or all of his innovations in either direct copy or in some modified form.
In one instance, Mauser sued the US Army (and won) for the Springfield M1903 because of violating Mauser's patent.
In other areas, using multiple locking lugs has become the standard for most locking breech rifles. Mauser used a setup of 2 lugs on the front of the bolt with a spare/safety lug towards the rear of the bolt in case of failure of the lugs in the front. As strange as it sounds, before Mauser there were rifles with only 1 or no locking lugs and this meant if a lug or whatever locking mechanism failed, the bolt comes flying back into the shooter's face.
Another concept/innovation copied from Mauser is venting gas away from the shooter's face. In his day, ammunition case were notorious for rupturing. While it didn't happen with every round, the frequency was high enough that there was a real danger of super hot gas from a ruptured case blowing back into the shooter's face. Think of a blowtorch blowing in your face and you get the idea. Mauser designed his G98 in such a way that gas from a ruptured case is not only redirect away through vent holes, but was shielded to blow away.to the sides or upwards. This idea in a different form is used on the AK47.
So while not every bolt action rifle is a Mauser action, it would be very hard to find one that is not influenced by some aspect of Mauser's G98.