Their Alpha* work from DeepMind is actually quite good and has a good track record. LLM/Gemini - yeah, what you said, I wouldn't trust a word their team says.
I will point out that Physics and Chemistry are awarded by the Royal Swedish Academy of Sciences while the Peace Prize is awarded by a separate Norwegian committee, so it is plausible that one would be more respectable than the other. Literature is a completely different institution as is Physiology/Medicine.
The Peace prize and Literature prizes have far more questionable winners in my view than the Physics and Chemistry ones.
Economics wasn't added until the 1970s, and has had some extremely suspect winners.
For now, this is not so much about being "respectable", as about the prizes given in the Sciences are not so bound to ideology or politics.
AlphaFold/AlphaProteo is genuinely a major breakthrough in biochemistry. Now if they start to hand out prices in Physics, say, based on it's importance in promoting some specific ideological agenda, then I would be wary. (For instance if they give the price in Physics for "making the the field of Physics more relatable to transwomen in the Middle East".
Some people see it as obvious that hard science and politics have glaring differences that makes the meaningfulness of an award for being very good at one or the other very different.
The Nobel committee picks candidates for all the prizes, and the final decisions are split up over four different institutions.
The only argument I could see along these lines would be favoring the Royal Swedish Academy of Sciences in particular, but that would mean that chemistry, physics, and economics count but medicine doesn't count. And that's just confusing.
Aside from the fact you're conflating two very different things comparing this to Gemini, what exactly is the problem with the Gemini?
Specifically just that the release was a bit awkward and had some problems? I've found the latest model releases to be very good compared to other frontier models.
Probably a reference to when Google was widely perceived to rush out the first Gemini release, neglecting to mention it did lots of weird racist stuff.
A Nobel physicist that couldn't do basic arithmetic would definitely raise my eyebrows, but even taking your analogy at face value Gemini was not marketed as fast food slop. Google can't be trusted to hype products in a reliable way, regardless of their technical details.
It's trendy for accomplished people to talk down about themselves as a way to sound cute. It's similar to software developers who like to say "I don't know what I'm doing, I just Google and Stackoverflow all day." It has a certain charm to it, and certainly there are some people for whom it's true, but overall it's just a misguided attempt at being modest but ultimately a horribly misleading statement.
"Do not worry about your difficulties in mathematics, I assure you that mine are greater" - Albert Einstein