How does hybridisation affect an otherwise chiral centre?
I really wouldn't put too much stock into YouTube comments. Often, it's just the blind leading the blind. The comments on this video have all sorts of incorrect statements, it's really not where you want to be learning from...



Firstly, chiral centres are not restricted to only carbon. Source: IUPAC Gold Book. With that out of the way, we can enumerate the three main possibilities for nitrogen.


$\mathrm{sp^3}$ nitrogen with a lone pair is usually not considered to be a chiral centre, as the rate of inversion is very rapid (google "nitrogen inversion").

There are exceptions, such as if the amine geometry is constrained by a bicyclic system (something similar to quinuclidine), but that's a discussion for another day.
$\mathrm{sp^3}$ nitrogen without a lone pair e.g. in ammonium cations, can be chiral if there are four different groups attached. So these two molecules are enantiomers of each other.



In fact, it is this context in which Wikipedia says that nitrogen can be a chiral centre.


  Racemization by Walden inversion may be restricted (such as ammonium cations), or slow, which allows the existence of chirality.


The implication is that nitrogen inversion is fast in the case where there is a lone pair. However, it is very unclear, so I don't blame you.
$\mathrm{sp^2}$ nitrogen, e.g. amide nitrogen, is planar so it cannot be chiral. So, this video you watched is incorrect in stating that the amide nitrogen is a chiral centre.

And, that also means the comment you quoted is correct. But, I would caution that it is not a direct cause and effect relationship between "$\mathrm{sp^2}$ hybridisation" and "not a chiral centre". It is more like: because it is $\mathrm{sp^2}$, therefore the geometry around it is planar; and because it is planar, it cannot be chiral. 




As was mentioned in the comments, phosphorus and sulfur behave differently. This has been covered multiple times here; here are some links. 1 2 3 4