Bejeweled over Castlevania? Isn't Bejewled Extremely Derivative? Why not Bubble Bobble.
While it wouldn't be the first puzzle game i'd think off, certainly not before Columns, Klax, Puzzle Bobble, it is a big franchise (50 million sold by 2010, obviously a lot more now) and it started the whole Match 3 Fad. There were and are thousands of copycats jumping up everywhere from straight up clones on google play to more interesting titles. It definitely belongs in a hall of fame but not before the other puzzle games that existed. Not before Klax or Colums that did all that connect stuff long before.
Personally, I'd consider these sorts of experts far more capable of making selections in this sort of process based on history and cultural influence than the kinds of industry figures you're suggesting. In the end, there is an exhaustive list of games that could be nominated or inducted. This is just one organization's selections.
I would say it depends on who these "experts" are. There are video game "scholars" in the way there are archaeologists or historians or scientists. In the end it might be some ex-ign morons or some random youtubers (god forbid some clueless people like the AVGN or Pat the NES Punk)
The problem is that the foundations are ignored. Rogue gets nominated once, when it should be in there from the start (especially considering today where tons of games are "roguelite" or "roguelike") and Starcraft first and Warcraft never even mentioned? Without the success of Warcraft 1 & 2, Starcraft would not even be a thing and Warcraft spawned World of Warcraft.
And tons of games never mentioned that should. I would put Wing Commander in there, given the fact that it pushed technological boundaries, is popular enough to spawn mods, was in the Guinness Book of World Records (WC3 and then 4 as most expensive video games until Shenmue) and where the reason why the whole "space opera" genre even exists (Colony Wars, Freespace, Freelancer, Starlancer and so on)
Same with Half-Life (shouldn't that be first ballot? influenced, the mods (counter-strike!), the culture about it, it made Valve and led to Steam and for over 20 years people ask where Half-Life 3 is)
Again, i just look at it, i don't claim to be an expert, but i definitely shake my head at those weird choices and nominations.
And then there's the induction of Barbie Fashion Designer...what exactly did that influence or how did that have any longevity?