Another pic:
Exploded chess pieces!

Plaster is pretty boring/stable stuff, not expanding or outgassing appreciably. A couple of minutes Googling however indicates that Tenite is prone to decay.

I have lots of tenite stuff and this is the first time I have seen this. I also have more than a few filled sets where the plaster has extruded visually to extend beyond the baselines of some of the pieces. I suspect in this case that someone added something to the plaster (for whatever reason) that is the culprit (maybe a glue of some sort - I once had a Drueke Player's Choice that someone had filled with glue of some sort that had essentially melted the pieces - I bought it for the weights and stripped those out for replacements). It is also possible that this set was stored in an attic where everything would have gotten really hot - especially the pieces in a contained case. None of the bakelite pieces seems to have suffered at all - but one of the reasons bakelite was so popular was its heat resistance.
I have encountered some celluloid pieces (usually dice but a few chess sets) where they have basically caved in on themselves - which is a weird form of decay that celluloid can undergo and that can actually spread from piece to piece, (I don't collect pool balls so I haven't run across any of the infamous exploding celluloid pool balls.....)

Im not doubting that most of the tenite that you own is fine, but I suggest you google tenite deterioration, as I did, it returns a fair number of pages in which conservators describe problems with it deteriorating. Plaster expands as it sets, so the appearance of overfilling is not a surprise.

I have many many tenite sets (literally in the hundreds - I have a couple hundred of these combo sets - probably half of which have gallant knight sets in them) and this is the first like this I have ever seen - and by the pictures the pieces didn't decay - they exploded - I had to take the divider frame out of the case to get all the bits and pieces out since they had jammed in the crevices. Celluloid is much more problematic.
I have filled chess sets (in my misguided youth) with plaster and any expansion occurs while setting (which only takes a short while compared to say concrete/cement - I did that for a living for awhile) - at which point you scrape it level before attaching the felt.
(Curiously enough I have one Crisloid combo set that reccomends sugar as a possible filling for the chess pieces - many of the Crisloid sets came with caps that slipped over the pieces.)
(You can see the green caps to the right of the case.)
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I got this combination set awhile back. If you look closely several of the chess pieces are really damaged - the pawns in particular played Mount Vesuvius. They are a Gallant Knight set which someone had filled with what I presume was plaster of paris and at some point it continued to expand and likely off gassed (which blew the tops off those poor pawns). Gallant Knight pieces of that vintage were made of tenite which is normally a stable plastic. Worked out for me since I got the whole set (with a lot of bakelite pieces) cheap - I just threw in a factory weighted (with metal slugs) set - they are pretty common and fairly cheap.