He probably should run this by his own attorney, especially since we cannot read the entire document. My reading is that he is simply renouncing his right to be a co-executor, not his rights to anything that may have been left to him in will.
Not everyone wants to work with someone else on such a task.
For one, thing, the executor is entitled to collect a fee for the work done. However, the executor may have to split the fee in any situation where there is a co-executor.
Other people, simply dislike having to work with someone else on such a project. Quite often, in these situations, one person winds up doing the lion's share of the work and then that person resents the split, which is typically 50-50. Then, too, some people simply cannot get along and the probate process drags on while the probate court resolves disputes between co-executors, etc.
Even under ideal circumstances, when there are co-executors, usually both have to sign off on anything major and that can be inconvenient, especially in any situation where "time is of the essence", as may happen in real estate transactions involving the estate.
Personally, I did not name co-executors in my will because of the above issues. Seemed like more problems than solutions to me.