Some very scary felling going on in these vids!!
The debate on wearing gloves is a big subject, the saw has two safety features which should stop the chain catching you if it comes of the sprocket and bar, a chain catcher and a flat plate on the bottom of the handle, if the chain snaps in my experience it just thows it off the end of the bar. Gloves do have protective padding on the back of the hand and will help, but propper training, work positioning and safe use of the saw IE understanding kickback and using the dogs teeth when cutting will help.
tbh gloves wont stop you from getting white finger, the only thing which will help slow it down is a well maintained saw, sharp chain, anti vibe system in the saw and HAVS checks on the saw which will let you know how long you can use the saw in a day, but even that is a guide as it will differ in different work conditions.
All in all trainning common sense are the order of the day!.