I imagine it was either an encoding error or a random clip accidentally left in the output timeline. Probably similar to the out-of-place shot on the initial pressings of the Star Trek II Director's Cut BD; just that no one caught this one until much later.
There is no kiss in the missing footage. Here's the original scene from Singin' in the Rain:
The footage from 3:37 - 3:42 is missing on the Blu-ray of That's Entertainment Part II, while the footage from 3:42 - 3:47 plays twice. On the laserdisc of TEII, the scene from SITR played out...
There's a few seconds of repeated footage during the Singin' in the Rain segment. Kelly and Charisse appear to do the same move twice (it's the first time that's in the wrong place).