Here's a pretty good video of the Taoist Tai Chi 108 form: Our Founder Master Moy demonstrates Taoist Tai Chi arts. - YouTube
As you can see there is a lot of obvious stretching, like a single whip (for example) has some lean-forward. I know that breaks the basics of Yang, but that's the nature of Moy's style.. Its physical health implications are found by new students fairly quickly; it is a very accessible form for that reason. None of the stretches are unnatural/too 'yogic' though. The intention of the stretch is for strengthening inner organs like practices of qigong. The psycho-spiritual benefits come gradually.
Other movements in the form like wave hands like clouds, snake creeps low, and golden rooster are more recognizable Yang. I know some people who started their training with the TTCS and eventually made the transition to traditional Yang fairly easily.
I wish there was a video of the lok hup online. I know that would showcase Mr. Moy's skill more than the 108 Taoist Tai Chi. I never knew Mr. Moy, but I've seen some of his students (the current advanced instructors) lead lok hup sets and it's impressive.
All respect buddy but from the clip presented that really is not very good Tai Chi there.
Fair enough none of us can tell what's happening 'inside' but the moves on display aren't necessarily best conducive of Qi flow.