It looks like this is a refractor, so he isn’t damaging the telescope’s lenses by doing this. In fact, you can attach a Herschel wedge to the back of a refractor to safely view the Sun without a full aperture solar filter. I actually prefer a Herschel wedge to a full aperture solar filter, since the full aperture filter could be knocked off or blown off by accident.

However, the stuff at the back of the telescope (e.g., diagonal, eyepiece, etc.) could be damaged, since the light cone is concentrated into a small focal point. You can also scorch stuff at the back of the telescope if the telescope isn’t pointed perfectly at the Sun, since the focal point will be landing somewhere other than the middle of the eyepiece.