It does not appear to be an S-300 battery
The question is: "I am not a military expert but can someone identify a system in such a video?"
Short answer, yes.
Long answer: ideally, anyone attempting to identify vehicles would want more than just a few seconds of video compressed to near oblivion. Context, in the form of video of the surroundings would also be preferable.
However, it is a fairly quick job to say what it is not, and as far as I can tell from the video, this is not an S-300 system being attacked.
- (00:03) Obviously a Main Battle Tank being attacked. Not any vehicle in S-300 family.
- (00:24) Two turreted tracked vehicles with long gun barrels. Very likely MBTs, or possible some kind of infantry fighting vehicles. Also it has infantry moving with them. Not any vehicle in S-300 family.
- (00:44) Hard to make out, but it obviously has a rotary antenna, and what looks like one large and two smaller flat panels. This matches none of the vehicles in the S-300 family.
- (00:55) Even harder to see, but it does appear to have a smaller rotating antenna, and one can clearly see a big flat area, a circle with cropped sides.
- (01:10) Again a rotary, and again, a vertical flat area flanked by two smaller.
In none of the three later, there are any other vehicles shown.
Of Armenia's Defence Forces, there is only one system listed that matches the look seen in these videos, and that is the 9K33 Osa NATO reporting name: SA-8 Gecko.
Image source: Wikipedia
"Are there any other sources (videos, combat reports, etc.) that confirm the report of the S-300 being destroyed?"
In the video in the article — mirrored here — this does not show any destruction, only that someone is looking at these systems.
And there is this video, again, nothing is shown being destroyed, and one vehicle in that video — definitely — is an 9K33.
So in conclusion: Yes, such a video can — by a skilled observer — be used to make a good estimate as to the identity of vehicles and other weapons-systems being attacked.
But — no — that video does not, nor does any others out there, appear to show an S-300 system being attacked and destroyed, and even less so with any kind of distinguishing identifying information of attackers and attacked.