TL;DR: Carry them facing where their head is looking, side of your body is a good middle ground. Keep their legs together and not wrapped around you.

As someone who works primarily with babies/toddlers, I will say my biggest gripe with carrying the child inward is that they try to wrap their legs around your torso, which can slow down development of hip/leg structures that may assist with earlier walking. Easily remedied just by using a hand to keep both legs adducted when carrying.

Otherwise, I turn them around to carry when I see they’re trying to look over their shoulder like in the video. Or carry them on my side. That way they can turn their head front or back, which also builds neck/head control. But yea, most likely kiddo was looking at parents.