It DOES sound like a parody of Slavic languages, possibly Russian, but the rolling Rs are missing - that's a very obvious characteristic of Slavic langauges!
I can hear that this is not a genuine language and that they are making it up.

However, I can't tell the difference between ANY Slavic languages other than Russian and Polish (and as of lately, also Ukrainian and Belarussian.)

I couldn't say whether someone was speaking Czech or Slovakian or Serbian, Slovenian or Bulgarian....

I have learnt to recognize Romanian - not hard. But that is not really Slavic language, it just has some slavic words in it.

Can you Russian speakers differentiate between those langauges?

But pretty much all Western European languages are immediately recognizable, even if I don't speak them. A few small minority languages would be unrecognizable, but none of the national languages.