These typewriters are rare, so you're going to have trouble digging up much info. There's an old advert here which says they use the same microprocessor as the IBM PC. Since the large chip is also a DIP40, it's possible that it is an 8086 or 8088, although it could well be an 8051.
I was unable to find any additional info on the chips as marked, but I doubt that the part numbers were intentionally obfuscated. Given the era, and the fact that IBM was involved, I would make a guess that the chips were a custom order, which is why they have unusual markings. It could well be that the main chip is an 8051 or some other DIP40 MCU that came with a custom ROM from the factory.
There's a pretty great guide to vintage Intel chips and yours don't appear anywhere on there. CPU-World also has some great info on old Intel MCUs and CPUs. Unfortunately I was unable to find anything that obviously matched.
If Y1 is a crystal that is connected across pins 18 and 19 of the DIP40, this is a hint that it's probably an 8051. If Y1 is instead a standalone oscillator that provides a 12MHz clock signal to pin 19, then it might be an 8086/8.
Another quick test would be to see if both pins 1 and 2 are tied directly to ground. On the 8086/8 this will be the case, but on the 8051 pin 1 is P1.0 instead.
It's interesting that the 4-digit numbers (8502, 8506, 8510, 8514, 8516) seem to be duplicated across chips from different manufacturers and in different packages. It's possible that these are internal references to IBM project numbers, which would make some sense given the layout.
Whatever it is, it's probably quite rare, and it'd be great to see it documented!