can royal gamma be in the same tank with mystery wrasse?

Should be okay. I had a RG with a MW a long time ago and the RG will just hang around it's hiding hole while the MW swam all over the place. Once in a while if the MW gets close to the RG, the RG will open it's mouth wide and the MW will just be on it's way.

Most important I guess would be tank size.
 
Assuming you have ledges or caves that the RG can claim as territory, you will probably be ok. RG do protect their "hidey hole" but do not go out of their way to harass any other fish. Mystery Wrasses are occasionally intolerant of fairy and flasher wrasses but should not perceive a RG to be in their ecological niche.
 
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