Is it to "catch" the ship or to act as a brake to slow the ship as it slides into the water?
From what I've seen in videos it seems to be the latter rather than the former. With a very heavy ship, I would think that a "catch" would simply tear the chain anchor point out of the ship or the dock when the chain went taut. OTOH, a slowly moving ship could be restrained by a stretchy tether such as heavy rope.
In this video of the launching of the Queen Mary...
the use of drag chains to slow the ship is mentioned at approximately 3:45 minutes into the video.