Man on Linux runs groff, which (like the original nroff/troff) is a fully general macro processor in addition to being a typesetting system. I wouldn’t bet on it not being able to launch subprocesses, or especially on it having no overflows and such on untrusted input. I’m not even sure about OpenBSD’s much more limited mandoc.

(Also, I don’t know about ffmpeg as it is somewhat more rare to have it be public-facing, but there have definitely been exploits against ImageMagick, usually targeted at websites using it to process user input.)