You and I are in the minority on this, I think, but you are still right. It is a commonplace for both "caring" hobbyists and "uncaring" scientists (I was reminded earlier, by a post of Peter J.F., that an aversive reaction by mantids to flies can be induced in the lab by zapping the mantids with an electric shock every time they strike at one.. Now that is stress!). And yes, the life of insects. like that of humans, is shortened by stress, whether or not the subject is physically injured.
@Morpheus: If you were cornered in an alley and threatened by a couple of giant yobboes, wouldn't you feel just the tiniest bit stressed, even if they didn't actually tear your head off?
As to whether the behavior shown here borders on "mistreatment' or not, it is worth remembering that the author of this clip was banned from this site for lying to and cheating members here, so I don't think that he would worry unduly about a little mantis mistreatment.
Addendum: Before some well-meaning member suggests that stress is an emotional response to a perceived threat, I'll point out that I am referring to the biological concept pioneered by Selye, long ago. In this context, our mantis would first perceive a threat to its life and react with alarm that would be manifested by a "flight or fight" response. The former is less stressful since the mantis (as happens with nymphs) would either run for cover and escape or get killed in fairly short order.
If the response is resistance, the mantis may still escape or be killed, but prolonged resistance without either outcome will end in exhaustion, and in the case demonstrated here, the stress can be continued indefinitely or until the tormentor becomes bored or the mantis is too exhausted to defend itself any longer. Yep, that will shorten its life all right.