mickey,
When I lived in Taiwan and trained Mantis (and Long Fist), I never saw anyone 'grab into' a punch; only having the already-closed (or partially closed) fist tighten fully prior to impact. And I never experienced, nor saw anyone, hurt their elbow while punching. You hurt the elbow if you habitually hyperextend it. Proper air punching should still leave a small amount of bend in the elbow. If it's done right, the arm can appear to fully extend, but there's still maybe an inch of bend, which isn't even noticeable. Another method is to recoil slightly without extending as far. A lot of it may be personal variation.
I don't know how practical 'grabbing into' a punch would be from an application standpoint. You cannot always gauge exactly when the moment of impact will be against a moving person (or heavy bag), if the hand begins as consciously open like at 48 seconds into the vid. Time it, angle it or distance it wrong and you'll have a busted hand. I simply don't feel it's natural in the heat of the moment.
I had a good friend in Taiwan, surnamed Kuo, who was an excellent Long Fist man; he could fight very well, and (IMO), he had the best Long Fist form I've ever seen. What set him apart to me was his precision, spirit, and the speed/power/explosiveness of his punches/strikes, kicks, and overall movement. He wasn't a big guy, looking more like an academic than a fighter, but his forearms were thick and I've felt the power he could generate. A rather large British MAist friend of ours referred to Kuo's punches as 'thunderous'. He also understood what the moves were for. He never grabbed into a punch like in the vid.
Despite his outstanding form, he didn't place forms on a pedestal like many practitioners did, which is ironic in a way. He also hated when people complimented his form; it made him self-conscious because he preferred application and sparring. I tend to think his fighting carried over into his form, not the other way around. A pity he never became a teacher, and I do know he stopped practicing a long time ago, and became a university professor in Taipei.
*edit to add:
I only mentioned Kuo because there's a fine line between (1), power and gracefulness, and (2), becoming dancey-prancey. Especially in some Long Fist styles. The prancey types tend to lack a combative focus in training and be almost exclusively forms-oriented. There is also usually little to no understanding of application principles. This can come across with a lack of spirit and 'urgency' when they perform, almost like moving by rote, or sleepwalking through it.
BTW, Henry Gong's rendition of that set was excellent. Totally different level from the first vid.