I think a beta is many different things -- frequently not all in one person. A beta may...
1. Toss around ideas with the author, helping her find a direction for her plot, or suggesting elements she may have overlooked.
2. Look for insufficiencies in the story -- "You need more xxx, and you need to strengthen yyy, and I think zzz is much too vague.
3. Look for plot holes, or things that don't mesh. I see this as a little different from #2, more black and white. Like, I once noted that using one bedsheet was not enough to excape from a 3rd-floor window. Or, the OC has this characteristic early in the story, but the opposite later in the story. But that's more direct than #2, not as nebulous.
4. Fix grammar -- tenses, run-on sentences, overuse of passive verbs, etc.
5. Oversee appropriate language / local idiom use -- Doyle and Bodie will use a lift, Jim and Blair will use an elevator. For this, it's wise to have a beta who's a native in the particular style of English being used.
6. Recognize and fix spelling. Not different styles (honor/honour are equal in my eyes), but things like to/too/two, or site/cite/sight, or simple typos.
7. Give the author a second opinion of the effectiveness of the story, or if something feels "lacking".
As I said, not every person is equally adept at every beta skill. I'm pretty strong in 3, 4, 5, and 6, but absolutely lousy at 1, 2, and 7. Therefore the authors I beta for, have another beta who helps with those aspects.
Gatekeeper for an archive? As in, is this story worthy of being included? I would consider that a judge, rather than a beta, or just an "Archive Mom". Somebody has to make the decisions for a small archive, if it has standards more exclusive than "come one, come all". But, unless they make suggestions about the story, I wouldn't consider it to be "beta".