If not that, it could be his HDD. If the replays are saved on the Hard Drive, he is accessing the hard drive to replay the data. If the HDD is slow(5400 RPM) or near full, there will be some slow down when accessing the save.
But this also depends on the format of the saved file, and the in game replay player software.
All I'm saying is, I think it's a Blizzard issue with their fresh beta, not a your friend's rig issue.