I found out what happened. Evidently, when Adobe changed the location of the Device Type report over to the Mobile group on the Reports page, it also affected the visibility setting on Video & Mobile Reports access:
As a result, I've had to go into my User Group settings to update any with Custom settings to place a check in the box next to Device Type. This was a bit frustrating, as I learned a good number of my User Groups were affected. I'm actually surprised more people didn't ask about this particular issue.
No custom menus or anything. It's just disappeared from his menu. I even asked him to log out and back in, and it did not reappear. I've seen on occasions where items have disappeared and reappeared from menus when switching between different report suites while logged in, and the only way I've been able to reconcile it is by logging out and then back in. I have other users with similar access who can see the report, so I've got Customer Care taking a look to see what's causing the issue.