I barely looked at Adobe Reader so not sure about that one, it definitely does not work with this PDF though, likely because it's not compliant in several ways. Besides that I wouldn't be surprised if it supports all the required JS APIs and more, just possibly behind some permission prompts.
It might work in Foxit as I believe it supports some scripting. Most of the other native PDF renderers are more static, as far as I know. In either case, I was most interested in the browser-native engines, as I always thought of them as more "static"/limited.
As for documentation on specific features: to be honest, I just looked at the implementations of PDF.js and PDFium. Both only support a subset of the "standard" API, likely for security reasons. But PDF.js for example allows changing a field's background color (colored pixels!), and PDFium allows modifying their position/bounding box (I tried a high res color display by moving a row vertically as if it's a scanline, but things become quite laggy).
Great work! We had the same idea at the same time, here's my version of PDF Doom:
Source: https://github.com/thomasRinsma/pdfdoom
Playable here: https://th0mas.nl/downloads/doom.pdf
Yours is neater in many ways though!