Ahhh... Seeing Guy, all I could think of was "Snoopy, eat your heart out!"
Guy, I believe is a very big part of Harry and Meghan's life and with all the different events going on with this wedding, perhaps HM invited Guy to come stay at Windsor until the festivities are all over and the couple return to Nott Cott.
Looking at Guy in the Range Rover with the Queen, the scenario that went through my mind is the Queen talking to Guy during the ride stating "Now, I'm taking you to visit for a while with my good friend who helps me look after my own dorgis. You be nice to him and behave yourself." (gives Guy a treat).
Not only is Meghan thoroughly embraced and welcomed into the family but after the Queen saw how her furbabies took to Meghan right away, she had no qualms about inviting Guy for a stay.