"doydum" means "I have had enough" or "I just became full". It is a verb, meaning that it describes the action of becoming full. However, "tok" is an adjective, describing your general state of being full.
I have a different question. Çocuk changes to çocuğuz i.e. We're children. The k changes to ğ.
But here, tok changes to tokum? And not Toğum?
Does it only work for plural first person terms? Or is there something else that I am missing?