This kind of sentence is common when you're making a distinction between two related ideas. In the example above, the bouncer says:
I don't set the rules; I just enforce them.
This is something that employees of a store or company will sometimes say when people ask them to change a rule that they're not allowed to change. Some other examples include:
I don't hate him; I just don't want to talk to him right now.
I don't force him to take lessons; I just encourage him to stick with the things that he likes to do.
When you pronounce these, place the most stress on the verb in the first part of the sentence:
I don't force him to take lessons; I just...