Because I'm specifically defining "complete" to not include "DM brain" adjudication. If anything the DM makes a decision on without reference to the rules is actually part of the ruleset, then every RPG is actually complete.
Not saying you can't define it that way (we're just debating semantics, of course), but I feel my rather asymptotic definition of completeness at least has a little more utility.
Fair, but I don't think you'd get much buy-in as a general rule; there's a difference between
specified ad hoc adjudication, and "there is no rule, so make something up" adjudication, which is what I was trying to get at.
If the rule is "DM Brain" (or coin flip, or whatever) that's a rule.
If there isn't a rule, then .... you can default to DM Brain (or coin flip, or whatever). That's ... different. And it's important to differentiate the two things.
I think what you're trying to get at is that there is a
specified method of adjudication. Because "DM Brain" and "coin flip" and "position of the moon" and "call the first person named Jake in your contacts and get their binding answer" and any number of outside referents are still valid methods of specified adjudication.
Which leads to two separate thoughts-
1. When people talk about 5e being "incomplete," they are usually discussing an absence of further rules and complexity, not a method of adjudication. 5e has the tools to adjudicate - it's just too
simple for some people. They would prefer more- more subsystems, more tables, more rules for different kinds of combat. That's a different type of incompleteness.
2. When you discuss complete systems (like your coin flip system), you are still using background assumptions. The most prominent has to do with the idea that someone (player or DM) has to decide if something can be narrated, requires a coinflip, or if the coinflip is impossible. These are background considerations that can actually matter a great deal, but are usually subsumed under the rubric of "how the table plays," in most D&D games, but are more explicit in other games.
Put more concretely- who gets to call for (or veto) that coinflip can't always be assumed.