This is an accessibility function and happens because the volume slider has focus. If they made it so that left and right arrow keys always moved the video forward/backward it would break that accessibility and shut some users off from being able to use the website.
As annoying as it might be to someone who has full use of their mouse and keyboard it is imperative that websites can have all of their functionality accessed through something as simple as tab and arrow keys because that’s all that some people are able to use.
Note that I’m in your boat and find it to be annoying and just something to remember to unfocus after changing my volume, but having just recently been going through some accessibility training I can understand why this happens.
I don’t think I said that OP was wrong (in fact I’m pretty sure I agreed with OP that it was annoying as a fully abled user until I figured out what was going on), but to elaborate on my earlier point just slightly - once a horizontal slider element is in focus it will always use left and right arrow keys to move if they’re pressed. Up and down always works to change the volume because there are no other elements when the video player is selected that are waiting for an input.
If they made the volume slider vertical instead of horizontal it would end up working actually better in this case (because the vertical slider would instead wait for up and down arrows), although that probably wouldn’t look as “nice”, but I’m not a UX dev so it could probably be jazzed up to look nice.