What do you call that person who wants others to behave like them?
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I'd call someone like that a moraliser...
...or perhaps a prescriptivist...
Most other words in this general area (conformist, traditionalist, conservative, etc.) are usually used to mean a person who wants to be like others, rather than wants others to be like him.
I would go for missionary and proselytizer
Another word is control freak (although this can be applied in a different context as well, and is rather informal)