Video is laughable
He rants on about how you should never approach a woman randomly
Then his example of grocery store is that the woman should cold approach the man
It is the job of the female to give signals for the male to approach. That is how nature made us.
She did not cold approach him she gave him a signal. In this case the signal was putting herself in his proximity. Other signals are a look or smile or erecting her posture etc when she notices you have looked at her then it is your job to go over and start a conversation.
If you are too nervous after you have shown interest with a simple non-threatening look and she responded with signals then make yourself scarce until you straighten yourself out as your lack of confidence will turn her off.
As far as what to say do not overthink it. She is interested so do not over worry about it.
Cold approach if you want but be prepared for rejection. The same thing goes for the female if they cold approach
She could just walk up to you and say she is interested in you because (then state the reason) but that puts her in the very vulnerable position of being rejected and puts you in the awkward position of doing the rejecting.
Signaling is the merry dance of nature to avoid rejection. It also keeps women from being bombarded by guys and visa versa