No, the wording of the terms specified is one sided. They only have the right to terminate with immediate effect or with a shorter notice period as long as they pay the notice period salary. There is no automatic equivalent right for you just because they have for themselves.
Even if they have accepted a shorter period for someone else, does not mean they are forced to do it for you also. Similarly, a decision not to enforce a particular right is not a waiver of the right and it can be enforced later or for a different incident.
Even if they have accepted a shorter period for someone else, does not mean they are forced to do it for you also. Similarly, a decision not to enforce a particular right is not a waiver of the right and it can be enforced later or for a different incident.