The term "alternative reality game" has a definition. You (plural) picked the term because you thought it made for an amusing acronym in combination with the others and that's really the only thing important to your purposes; but "alternative reality games" are actual things; they have existed in a very consistent form for some time and that fact needs to be realized and respected. Further, there are terms which already much better describe the activity you're badly trying to shoehorn into the acronym.
The term also is nonsensical on its face. There's no such thing as "Live Action Alternative Reality Gaming", "bigfoot" or otherwise. All ARG's are "live action"; it would be like referring to the sport of swimming as "wet water swimming".
It's not a matter of what I "like" or do not like. You are now making retrospective trips to some ARG sources to search for information that you think can be interpreted in a way favorable to your use of the term; but you are failing in that regard, and having to invent rationalizations.
For instance, you continue to misconstrue the "denial that it is a game aspect" despite having already been corrected on it. And you misconstrue alternative reality gamers' resistance to stone-etched rules or formulae for the creation of their games for resistance to any acknowledgement that all (yes indeed: every one) ARGs that have ever been constructed and run have certain things in common that make them alternative reality games, as opposed to other kinds of activities. To wit:
1. They are created by a person or team of persons who writes the story and creates the game elements, and facilitates the game in real-time. Your "bigfootery", to tell from your definition, has no "game masters" or creative facilitators, only "players" who make things up by themselves for themselves as they go along.
2. The game actually has game elements intended to be used by the players - clues, codes, or puzzles, the correct decipherment of which allows the game's story to progress as planned and leads to the next plot coupon. Codes in particular are very common, although including them isn't some kind of rule - every ARG to this point has involved codes of some kind; the game attracts amateur cryptography fans more than any other type of player. Contrarily your "bigfootery" has no pre-planned plotline, and "players" create and place clues for themselves that they pretend to "find" in order to attract notoriety, clues which don't require decipherment and don't advance any plot. And no episode of bigfootery has ever involved decoding a cipher.
3. ARGs begin. There is a First Clue or inciting incident. In ARG lingo this is called a trailhead. This first clue is put in a place where it can be discovered by potential players. Once it is, deciphering the clue initiates the player into the game and provides information leading to the next clue. In your "bigfootery", players don't discover the first or any clues - they plant them, and then "pretend to" discover them.
4. The creative team does not use the word "game" during the game. However, players do, constantly, they're fully aware they're playing a game and freely admit so. Players also do not portray "characters" or play roles. In your "bigfootery" the players/creators pretend to "believe in bigfoot" and insist everything that's happening is real, with nothing but your claim that they don't really believe to say otherwise.
5. ARG's end. The story comes to a conclusion in which the antagonist or their plans are defeated or waylaid, or perhaps they succeed. Either way, the plot comes to an end. Your "bigfootery" does not end, because bigfoot can never be definitively found nor disproven, and therefore anyone can go out to the woods anywhere at any time and pretend to look for bigfoot. You might be right, that that flexibility and replayability gives your bigfootery certain advantages over ARGs, or you might not. But what it doesn't do is make bigfootery an ARG.
Despite all this, you are of course free to "invent" a game in which two teams of players bounce and pass a large rubber ball amongst themselves and then score by throwing the ball into elevated baskets, and call this new game "baseball". However, you should expect to encounter people who will take time to point out that 1) the name "baseball" is already used for a game that's nothing like you describe (and no, "it uses a ball that spends some time in the air and you score points so it's basically the same" isn't an effective rebuttal); and 2) the game you describe already exists, and it's called "basketball".
Everything you try to describe using the term "BLAARG" seems to simply be LARPing, if your theory is true. But I don't think it is. I think the position that nobody actually believes in Bigfoot and everybody who says they do is just "playing" your "game" is neither provable nor falsifiable, and is therefore basically useless in an empirical sense. There are certainly some people who don't really believe in bigfoot but pretend to, and plant clues and so forth; these are - as I already mentioned in the last thread - already called "charlatans". It's a fine word and there's no need to invent another.
Contrarily there are certainly plenty of people who believe that Bigfoot possibly or probably does exist. These beliefs may have been (likely were) influenced by the activities of the charlatans but that is irrelevant; the fact is there are many people who claim a genuine belief and no positive reason exists to claim they are lying. Some of these people go out into the woods hoping to find bigfoot, and genuinely misinterpret environmental cues and wildlife sounds and photographic artifacts for possible bigfoot evidence. There is also already an established and functional term for this behavior as well - it's called legend-tripping, it's not limited to bigfootery, and is a subject of some academic consideration.