There is no such thing as a “right to buy seats”. Everyone can reserve seats. You do not even need a ticket to reserve seats.
To travel on a train you always need a ticket for the route the train travels on. Tickets are for a route, not a train. You can buy a ticket between any two places in Switzerland, and it does not matter how many trains, trams, busses, cable cars are involved. And those tickets can be bought from SBB, even when other companies are involved. It is a common misunderstanding among people unfamiliar with train travel in this part of the world to believe that when you buy a ticket you buy a seat in a vehicle. That is not what you buy. What you pay for is to travel a route.
So you bought a ticket for the route St. Moritz to Zermatt, and that ticket allows you to travel on that route, on the trains that ply that route. And there are lots of other trains on that route. Tickets btw. do not need to be bought in advance. You could buy that ticket even just a minute before you depart… As long as you have it when you board it is fine.
Reservations are for a seat in a particular train.
On most trains there are not seat reservations. On some trains you have reservations. And on a handfull of trains reservations are even compulsory. The Glacier Express is one of those trains.
So you have two options:
- Use your ticket to travel from St. Mortiz to Zermatt on normal service trains. This will require a few train transfers, but is perfectly doable, and some people even prefer that, as those trains are often less crowded, and have windows that open.
- Get a seat reservation separately for the Glacier Express service you want to travel on.