What does this mean
The Black's Law Dictionary defines "exclusive right" as "one which only the grantee thereof can exercise, and from which all others are prohibited or shut out".
The clause you reproduce provides that the rights are not exclusive. This means that a party/obligee/grantee may subrogate (that is, transfer to someone else) his right, and the obligor or counterparty to that contract does not have the defense that "only the obligee has standing or entitlement to enforce that right".
Cumulative right seemingly relates to cumulative remedy, which the aforementioned dictionary defines as "a remedy created by statute in addition to one which still remains in force". This means that a party's exercise of one of his rights does not preclude the exercise of his other rights.