In the first clip, Rose Marie is indifferent to the Sergeant, until he starts to sing. You can see her thinking, "oh, he can sing...I wonder if he plays an instrument...hmmm", because, as all women know, if he can sing AND play, we are but putty.
The two have an unspoken attraction; a look from across the room, their eyes meet, oh no, look away, is he still looking?, look back and on and on. They "fall in love" without ever having to touch or even speak to one another.