I noticed on some game pages for example Time Crisis there is a time record but no video file or link to see the run. I can't tell if a runner hasn't got to upload the run yet or a possible glitch with the links. is this common to have records but no video to show it?

It depends on what the moderators have set. Some games require proof, some don't.

Then it's not really a valid run, is it? At least a screenshot of final time should be required imo.

"imo." Precisely, that's your opinion. :P I'm perfectly fine with users submitting times without proof if they don't have a pretty good time, but once they hit a certain level I'd prefer to have proof. In some games (i.e. P4), there's no real competition so they don't really need it.

Many communities only really care about proof if you have a top time. If runs are to be taken seriously they should have a full video though.

Validity is subjective.

Also some runners are trusted.

But yeah, there are entire communities that operate without videos. It's really common in Japan, for example, to have a time without a video.