Never seen one like that, and I've had many of them.

Here we go.

EDIT: It's a 2nd print, with the TSR Wizard logo + fixed picture glitches.

I was struggling to get a photo to show the gloss under my lights, when I realized the glare from the flash would – for once! – be useful. Here it is, laid on top of a 3rd print A1 I had on hand.

Can you post some closeups of the fold lines and edges/corners so we can see if it's laminated or coated?  It does look like it's coated, and it appears that the blue is lighter than typical, which could be the result of a semi-transparent coating or laminate.  Might be significant variation in the ink color too.  It also could be a different cover stock was used for a few.

As far as I'm aware, lamination requires a border of laminate where the two sides seal together.  Basically enclosing the paper in a plastic bag.  The laminate does not seal, stick, or bond with the paper itself.  So my take is that this is simply a glossy paper stock on the inside.

We'd need to check other 2nd prints to see if they also are glossy, and if not, are there any other differences between glossy/non-glossy.

Foul

I am aware of laminates that do adhere to the underlying card, and would provide a similar effect when freshly applied.
However...
Thin adhesive membranes are modern. The ones available in the 80's were thicker.
If manually applied there would be evidence of them having been applied (depressions in the card).
Even mechanically applied (with rollers) by some guy who's dad worked at a printers, you'd still be looking at a modern application because all aftermarket laminate skins that I'm aware of fail at the edges eventually. The outer skin contracts over time and one of two things happens. Either the bond between the membrane and the card breaks down, or the card itself begins to separate.

To me, this has clearly been printed on different card stock. It may have been the remnants of a batch that was already in the machine and the new stock was just added to the top of it by a careless printer. It may have been an end of batch top up to complete an order (which would account a different cut if the guillotines had been set at two different times. Back in those days a lot of printers didn't have digital guillotines, which is why there was such poor alignment between text margin and paper edge in some of  the smaller print runs and smaller press items of the day. When I mean to top up and order, I mean lets say you order 1000 copies, and the pallet arrives and you have 1000 copies, but the pallet had been stacked badly and the corners of two boxed had been crushed, or a forklift driver had hit it with the forks. You go back to the printer and say, look I ordered 1000 but I only have 940 saleable. Do you want to send me another 60 or do you want me to adjust your invoice.

So it might be that we just haven't looked at these too closely and there are hundreds of them like that. Likewise, it wouldn't surprise me if this turns out to be an anomaly. Its certainly a curio. In fact, its in such good condition, I did consider that it may be a modern reprint. But if that were the case there would be other evidence in the scaling of the reproduction vs. the original (because one is a optical reproduction of the other, and optics are rarely equally accurate over both axes). It doesn't make sense to 'fake' a common module, but its not out with the realms of possibility that someone just wanted to see what they were capable of before looking at other products. At the moment I'll discount that last notion as extremely unlikely.

If I were looking for evidence of a modern reproduction in the booklet itself, I would start by looking at the clarity of the printed text and the printing of the illustrations. Are they crisp and clear? In the optical scanning process you get blurred edges and a loss of clarity. You then try to clean that up with software, either by considering each page to be a photograph and manually correcting the image (a very time consuming but successful a lot of the time) or by asking software to identify characters, erase them from the scanned image and replace them with digital text in the same font. This method can produce very clear and high quality digital files to print from, but the modern version of the 1980's fonts are often not identical in scale, and rarely identical in the actual placement of one character in relation to the adjacent characters, because digital placement of text is done with algorithms and to fractions of pixels (depending on how much you zoom in or out of the image).

I would then look at the placement of the ink on the paper itself (with a loupe). Ink deposited from a printing press is laid down differently from that sprayed onto the paper by a laser jet, and of course today almost everything we print comes from a laser jet. There may well be others who know more about these sorts of things that I.

One quick check you could do is to take a clear ruler and make comparative measurements across the page and up the page. Is the distance between the bottom of the printed text and top of the printed text the same? Is the distance between the extreme margins of the printed text the same? Are the distanced between the same points on the maps the same in both directions?

If not (bearing in mode they came from two different printers), particularly with the map, are the variations in scale identical? I.e. are the sizes of one map 1% bigger in both dimensions, or are they 2% bigger in height, but almost identical in width? Because if they are differently scaled in one dimension over the other, that is an artefact of optical reproduction. That doesn't mean its fake of course, just that one product was optically reproduced more times than the other from the original image source (the optical error compounds the more times something is scanned from something that was previously scanned.)