If I understand correctly, he want to move the "my games" subsection to the main game list section. I don't think it's a good idea. When I designed this structure I had in mind that games list is much more visited compared to "my games" subsection. Your change would save one page load, but it would bring unnecessary information to the game list screen, from the average section usage point of view. I stand by my design decision and want to keep current structure.
When doing design you must not only think of how you use this section, but rather how efficient is the section used in general.