"Run" or "modify" are not requisites in the common understanding of "open source"; legality of viewing is. "Open" to them usually means it can be distributed (to them) and read without breaking the law.
Says who? The Pope? Richard Stallman? Bernie Sanders? Some random self-appointed authority figure who goes by the name "the_af" on Hacker News?
Whose name is on the trademark application?
> Perhaps the open source movements should seek intuitive definitions of terms rather than invent vague nomenclature that only makes them unable to communicate with normal users.
The "open source movements" he/she mentioned have very technical definitions of what open source means (of varying degree, of course, but have you tried reading the GPL? Do you think it's non-technical?). Of all the valid criticisms you could throw at them, "vague nomenclature" is not one. Their definitions of open source may be difficult to communicate precisely because they are very technical, not because they are "vague".
I think "who" was quite clear in this context. Do you disagree?
It's unavoidable that people will be confused about terms outside their area of expertise. Since you mentioned gamers: I shudder at the vast multitude of confusing terms the various gamer communities use, like for example in WoW.
However, I think you're overstating your case: I suspect few gamers, if any, will confuse leaked source code or code which you're not allowed to use in any way as "open source". I don't expect them to undestand every nuance, but surely even they understand source code you're not allowed to run or modify is not "open" in any meaningful interpretation of the term :)