This sounds like my grandmother's living room furniture 50 years ago, all covered with clear vinyl plastic.
The remote control for both my MS-300 and MVP-871 did this. I had them both in saran wrap and clean. The MS-300 did it first, I asked the dealer if you would warranty it, since I dropped nearly 50K$ with them during that period. They got me a brand new HR-053 and an HR-052 for the MVP-871 since it had begun to peal. I was told it is a combination of sweat and chemicals (didn't say which,.. like skin cream, that disinfectant gel you use when people get sick to prevent germ spread by contact, and so on) coupled with use, since I used the MS-300 a lot more than the MVP-871. I have the Harmony H-659 that came with the MX-136, and used it for almost everything except the MS-300, and put the other remotes away. When I went to use the HR 052 for the MVP-871 it was sticky in saran wrap, had NEVER been used, after a year of sitting in the remote caddy, with no sunlight exposure, or any exposure. This time they wouldn't replace them for free. After putting up with it for a few years, I decided to use alcohol wipes ( the big ones you pull from the dispenser), with 70% alcohol and anti bacterial/scent/cleaning additives. After an hour of rubbing on the HR-053 AFTER I took it apart for the MS-300, all the goo coating came off, with a light layer of the gold leaf or whatever that says "McIntosh) at the bottom. This left the plastic a bit rough and dark greyish. So while it was disassembled, I used NuFinish and polished the plastic housing and button face, until the entire unit looked brand new, minus the goo or whatever that no slip coating is / they are made with; I believe I was told what the gooey stuff is for before it degrades. The Gold Leaf 'McIntosh' on the bottom and the odd letter faded slightly, but overall it looks really nice, like it should have brand new, and the finish and silkscreen letters are no coming off after a few years since I did the remote. Realistically I think the gold was already wearing from use and the goo was taking it off as well in the stickier places.
I'm getting ready to do the HR-052 for the MVP-871 now, which is how I found this thread, looking for a better way to do it. It turns out my way IS the better way...Just FYI, the technique is pretty much fool proof, for those who want to give it a try. It beats throwing out a perfectly good remote, then spending 100$ for one that will do the same thing sooner than later. The NuFinish step is important, (you might be able to use a plastic cleaner-polish kit instead) the micro beads polish and the polymer restores the plastic to a rich black smooth color after the goo is removed, plus removes anything the alcohol wipes don't. I use NuFinish for a lot of my restoration projects, anodized metal, magnetic tape heads, glass face plates, anything you want a nice clean slick rich surface that stays protected over the long run. As a intermediate step, every once in a while I use Pledge spray can Furniture Polish and a microfibre rag to clean polish and preserve the finishes on all my remotes, plus the MS-300/750 keyboard. I lost the remote for my MS-700 in a move, but the one for the MS-300 works great.
If your in the position of owning these type remotes and don't relish throwing away 100$ for each one, only to go gooey again, give this a try, it does really work and is easy, just takes some elbow grease and patience.. Maybe when I get the MR-052 done, I'll post photos of both..