I agree that there are some jokes, but it takes more than that to be a parody. I realize that colloquially, "parody" is a very broad term, but what I specifically mean by it is somethingt hat exaggerates aspects of a work in order to make clear some perceived flaw or absurdity already present in the original. The target of the joke must be the work being parodied.
From your list:
BBP wrote:"Live, on CD-Rom"
(since it's a CD-Rom it can never be live. )
Not a parody. In a sense, it's just factual (Torin interacts with the scene as it happens, so it's "live", while the game is on CD-ROM), but otherwise it's just a joke.
BBP wrote:"Phony Canned Applause" and "Phony Laugh Track" and "small fake chuckle" "fake crowd reaction" "small fake laugh"
The subtitles stress the canned applause is obviously phony
This is also just factual. Pre-recorded reactions are fake, so this just makes players who can't hear the audio get an accurate understanding of what's happening. Admitting the fakeness is admittedly humorous.
As for the use of the laugh track in general, there are many ways that
could be parodied. One possibility would be to have a laugh track for explicitly unfunny things (e.g. a tragic news report, a boring business meeting). Another would be to lampshade it, by having the characters themselves comment on it. Yet another would be to reveal that the laughter had been diegetic the whole time.
What the Bitternuts does, however, is just have various lines of dialogue that are just sort of lukewarm levels of funny followed by the canned laughter. It's not really subverting it or exaggerating it beyond the level of a (bad) sitcom.
BBP wrote:"With Jack Kluckman as Mr Bitternut.."
Obviously satirizing three stars.I still don't know who Kluckman is supposed to be.
Not satirizing. Just referencing.
Mrs. Bitternut = Sandra Bullhockey = Sandra Bullock
Mr. Bitternut = Jack Kluckman = Jack Klugman
Bobby Bitternut = Vinyl MacCaulking = Macaulay Culkin
I'll freely admit that I really don't know anything about those actors. However, I don't think they're relevant to the genre the Bitternuts is supposedly parodying. If we place in the 1950s, two of them weren't even alive then. I don't know if the Bitternuts are supposed to resemble the listed actors in any way. To me, it looks like it goes no deeper than "here are three names that sound a bit like the names of three actors".
BBP wrote:Toe tapping tune a la Nanny Called Fran, "here are the bitternuts, yes they're the bitternuts, they're not just bitter but they are nuts, they are nuts, bitternuts!"
TVTropes calls it Captain Obvious, this is to me satirizing the silliness of the summary of the pre-story in the titles, as you have in Nanny Called Fran.
That show is from the 90s, but if that sort of summary is also present in the those early sitcoms, then I'll grant that this could be parodying them.
Captain Obvious is also used to make fun of other things, like:
We join the Bitternuts just as they hear a knock on the door. {DRUM-LIKE KNOCK}
"We're now returning to the Bitternuts, already in progress"
(Captain Obvious)
For this to be parody, it must be the case that those early sitcoms tended to state the obvious
and the Bitternuts is making fun of them for doing so
and the Bitternuts is stating the obvious in an exaggerated way to call attention to how those sitcoms do it.
However, if the Bitternuts just state the obvious because it's funny, it's not parody.
BBP wrote:"Tune in next time to hear Bobby Bitternut say..." {cue random phrase}
How exactly are we tuning in next time?
I'd say this isn't even a joke. It's not clear in what sense the Bitternuts is a t.v. show, but it is one, and that's what shows say at the end.
BBP wrote:"The Bitternuts was (not) FILMED before a live audience!"
Yes? Some sitcoms have actual people watch the show as it's being filmed and then have their genuine responses recorded and used for the broadcast. The line here is just saying that it wants to brag about doing that, but includes the "(not)" because that would be lying and they actually just have generic pre-recorded laughter and applause.