Yes, that was Jacob Young in that clip. He played the role when Rick was a teenager from 1997-1999. He then left to do stints on GH and AMC for the next 11 years before returning to the part in 2011.
That would've been Agnes Bruckner as Bridget in the clip, and there have been 3 actresses since to play the role (occasionally played at present by Ashley Jones) since Bruckner left the role in 2000.
Most the time, shows usually never show clips of actors in the past, mainly because I think they have to pay them.
I always assumed that's why they're cut out or perhaps cropped out of a scene.
I'm sure they could have found a scene of Jacob Young from the same time frame that Bridget didn't appear in ... but that particular scene seemed to be his very first scene ever.
I think they've shown the clip a few times. If it's just a quick image with no dialogue (as shown), I don't know what the rules are in paying the actors.
Since I wasn't watching the show in 1997, I can't answer whether or not that was JY's very first scene on B&B.