How do we give user ability to create a request type for their section without giving them God rights to the whole site?
I don't believe you can. Within Setup > Techs > Tech Permissions you can allow your Techs to manage Locations, Parts and FAQs but I don't see anything for Request Types.
Sounds like a Feature Request required to support.
I don't think it is possible.
But one possible way is to give them Ticket import permission, in that way they can fill the template with the request type semicolon delimited and which will eventually create a request type based on semicolon delimited.. Also you need to keep in mind about the custom field if any,and add values later on.
Regards
Aakhib