There was a similar product someone got me as a gift a couple years ago. A subscription to vinyl postcards. I couldnt play them.
The problem wasn't that they were low quality. It was that they were too small. My turntable has automatic shutoff, where it lifts the tone arm off the record and swings it back out when the tone arm gets too close to the center. Considering how small these mini vinyls are, I suspect they will have the same problem and be unplayable on my turntable.
And yes, the article confirms that problem.
Try requesting a full export of your data... I'm pretty sure they have that feature (or at least used to... I haven't been on facebook in years). The note may be lurking in there, and while I hate how much data they retain, it would be great if you could get that back!