I'm sure they did it because the move gives them a better chance to win, no matter how insignificant it may seem. If it was the Jets, we'd have little to no issue with it.
To respond to a few: "I bet the Giants pick him up" - In the post season, isn't there a 9 day waiting period to clear waivers? Not sure on the exact number, but it is a lot longer than during the regular season. "Does he get a ring?" - Yes. He was active for 8 games, if they win, he gets a rin and 88,000, if they lose, he gets 44,000. The DE they signed off of the PS won't even get the 88,000 if they win, he'll only get whatever PS players get, I don't know the number. "This seems cold" - It is, but, he probably knew it was coming, Silvestro is probably signed for rotation on the DL, LOS gets very hot and muggy from what I've heard, the DL is going to suffer on both sides. He can also play Gronkowski's spot in the wedge on returns. Another thought is that they have possibly seen something about the Giants OL on tape and maybe want to try some kind of 5-2 formation or whatnot to exploit and will need more linemen. It is all gamesmanship, I am sure the reason they waited until the last minute as well was to give the Giants as little time as possible to prepare for whatever is the actual reason for this.