I found the religious imagery interesting, as well as the English lyrics.

And according to the Russian comments on the Youtube page, they're just as confused as we are. (Thank you Google Translate).

You said it much more succinctly then I did in my post below.

The Monkees. There is no meaning to this video. But its totally entertaining.
< src="

Not much of a mystery. The old Soviet Union often tried to copy western capitalistic culture; trying to make communism appear more appealing. "Look at us!. We have fun too!" These attempts were aimed at their own citizens as much as they were aimed at the west. It usually ended up appallingly bad as in the video in the OP or the infamous trololo video. In this instance, they were trying to copy western style rock music videos from the period. The imagery is intentionally weird - meant to appear as if there's some hidden meaning when in fact it's just random nonsense.

For example, check out The Beatles' I am the Walrus video. (Note that I'm not comparing them musically, there's no contest. I'm just giving an example of the kind of imagery I think they were trying to copy.)

Looks like they threw a bunch of stuff together and got their props from a garage.