In general, it's a bad idea to wear gloves when working with spinning tools. If the glove snags the wrong way, it can pull your whole hand into the tool.
For sure, but in this scenario I doubt snags pulling anything would be possible. In the video it was stopping the blade before it could even break the skin on fingertips.
If the safety mechanism failed though, the resulting injury would be far worse as a result of the gloves, so it might not be worth it in that regard.
The rules in my dad's wood shop when I was growing up were pretty simple: any jewelry (necklace, bracelet, watch, rings, etc.) had to be removed, and eye protection had to be on before a tool could be turned on.