Yeah, that's not it.There's a strong trend to reduce secondary (read superfluous) packaging, including gift packaging. Beyond the cost savings, there are strong environmental arguments in favour of it.
Look at the packaging - it's basically a blank version of the box it already comes in with a red ribbon in it. When it wasn't offered for free, it was expensive for what it was so no one bothered.
Gift wrapping slows down shipping speed and clogs the gears in distribution centers. If you look at any company that does still offer it, it's usually a crappy gift sack they charge you $5-$10 for. We've all come to accept the Amazon box as wrapping paper and no one pays for these things. If it was actual gift wrap - was would be a logistical nightmare, people might do it more.
Trust me, somewhere in that big Apple circle there were a team of many people and hundreds of emails all about this and an analysis on labor and time vs. cost and utilization - and nowhere in there was a mention of being green unless it was "We can cite a green initiative if the 5 people who ever used this complain."