Disclaimer: I don’t actually have access to this particular study so I’m working from the abstract and your question.

So working off of your shared link, it appears to me that the study doesn’t really change our present understanding on the origins of horse domestication and riding. Bitwear is often hailed as a telltale sign of riding, but this is problematic because horses pulling chariots also used bits! Bitting is only evidence of control from behind the horse’s head, and cannot be used to determine whether one form of horsemanship was preferred over the other. We generally need to look to other sources to determine that. Despite the inclusion of the word “if”, their statement indicating a shift from chariotry to riding strikes me as problematic as it implies that one was used before the other. We’ve yet to definitively determine which came first; and with our current understanding, it is probable that both technologies developed at the same time. Both were probably used depending on the circumstances. After all, chariots and sleds tend to be more difficult to use in rougher or wetter terrain, though they do facilitate the easier transport of more goods.

The only thing it really proves is that horses were domesticated and used by cultures at that time in that region (which is only a couple hundred miles from and 1500 years after the Botai culture where horses are presumed to have been domesticated and may have been ridden). Combined with other evidence such as depictions of riding, this study could be used as further evidence of the likelihood of cavalry; however, it does not prove the existence of cavalry on its own.

Was cavalry present around the 2nd millennium BC? Most likely yes as we do have depictions like this from further south around that time (but it’s also not been proven if riding was a technology that was shared between cultures or independently learned). That particular depiction also brings with it additional questions like what animal is actually being shown?