I can entertain the notion that some company did in fact have a rechargeable alkaline battery for a laptop-style computer back then. Yes we can agree that rechargeable alkaline is not a good technology, but it could hypothetically be economically viable. Some people may be stuck thinking of rechargeable batteries as we know them in contemporary products... that is, an internal, permanently installed, and generally irreplaceable part of the whole. This is the way modern cell phones, laptops, Chromebooks, etc. treat the battery. It wasn't always like that. Think back to your oldest Nokia cell phone (if you are over 40). It had a battery door, as did every single other battery powered product, rechargeable or not.
Imagine this: the hypothetical laptop-type device runs from (for example) 8 AA primary/disposable alkaline batteries, or you can buy the rechargeable pack. Those 8 AA's might cost approximately (example) $8. Single use. Imagine that the company offered its rechargeable pack for $24 (3 times the cost of standard alkalines, just for the sake of argument). Maybe they promised 10 to 20 charge cycles. Let's say a person could actually get 12 cycles from it. Then it costs the end user $2 per cycle. That sounds like a bargain compared to $8 for disposable batteries. If the cells were properly vented (like the "Pure Energy" brand rechargeable alkalines I remember from back then) and the pack itself was sealed well enough to mitigate any eventual leaks, then the concept could work. This rechargeable battery is not designed nor intended to last the entire life cycle of the product. It is a consumable item, but it still saves the customer money. Just consider that this is a possibility.