From my understanding HIV is a virus that infects immune cells and uses them to replicate. What happened is that this man had his immune system almost completely destroyed to defeat leukemia, and received stem cells from a donor with the mutation CCR5 known for its reduced risk of HIV infection.

Basically they destroyed the HIV's food source, and likely (at least temporarily) changed the man's new immune cells to the CCR5 variant in them that reduced the effectiveness of the HIV's ability to replicate.

Again, from my lay understanding, HIV changes its cell protein markers to avoid being attacked by immune cells. Often there are multiple HIV variants with different protein markers at one time active in a person.

IMO all but the 'newest' variant likely died of attrition, leaving one or two HIV protein marker variants that the new highly bolstered CCR5 mutant immune cells managed to latch onto and defeat.

I could be way wrong, but from my understanding this is the closest 'model' I can think of for how this would work. However, it's past my usual end-of-day so it may just be gibberish of an overtired mind.