Count the number of views
I believe the reason there is not common "Out of the box" solution for this, is that the statistics module has a long-standing reputation of ruining performance, as it performs a lot of database writes.

While it could certainly be "upgraded" to being entity agnostic, I guess there's little interest in doing so.

The most common solution then, I think is to use a tool like Google analytics for counting impressions, and exposing your video (or other entity) in ways/with urls that make their views easily countable in your tool of choice.

For Views integration, the easiest options seems to be Google analytics statistics, (Thanks Chapabu), but other interesting modules could also be GA counter, GA reports and GA importer