This video shows nothing but cooperative uchikomi practice. His form looks good to me, but we'd have to see him in randori/shiai to see if he's a competent Judo player. I highly doubt he's going to be anywhere near Olympic level, as is suggested by the title of the video.
Oh I don't know. You can see by his entries, uke control, execution etc that his level of judo is pretty dang good. For example, the execution osoto gari and ouchi gari against the heavy weight suggest knowledge of how to make those techs work against someone of different height/weight: they're on the fly adaptive
Someone who does 'good competitive judo' has a lot of the same tells.
As you rightly point out, we don't see Putin engage in any randori, grip fighting etc. Nor does his competitive career appear on www.judoinside.com
Finally, at age 57, he's probably a little long in the tooth for a sport in which the peak is 18-25 :S
So, yeah - it's likely just some media buzz. Or maybe they meant World Masters games?
Good judo though: to my eye, he's still very 'judo strong';