Haha, poor choice of words there. When he says "adding", he really means "apply a binary operation A • B, which returns A if ....".
The key point is: Once you can define a binary operation which is associative, and an identity element I for which A • I = A, you can consider using monoids.
The key point is: Once you can define a binary operation which is associative, and an identity element I for which A • I = A, you can consider using monoids.