I'm just speculating now.
I was watching
Mrmatty's trailer analysis and tend to agree with him on the multiplayer points. While I would rather have a singleplayer title just like every other Beth Fallout (NV, F3, F4) I could keep an open mind a multiplayer mode was done right.
Throughout the trailer you can see multiple hints that this is MP. You have the board game, as Mrmatty says with 5 players, along with that you have 2 chairs sitting next to each other one with a guitar one with a harmonica - obviously two people would be playing those. You have many other hints like the cafeteria with 2 plates set, and most importantly you have the computer terminal that says "You're Invited" - which I have to agree with Mrmatty here seems like thats how you can be invited to other player's games. I think Vault 76 will act as the central hub of the game, kind of like Vermintide 1/2 has their little hub - which you can probably customize. I predict you will be able to find, join, invite people through a central terminal, or that terminal shown in the trailer, and leave the vault to "Rebuild".
Thinking about it now, the setting of the game makes perfect sense to test the waters of a multiplayer oriented Fallout title. There isn't really any established lore for this period or area of US to really infringe upon and it's probably gonna be based centrally in podunk nowhere. If what one of my friends told me is true it could be based near and interstate which would make even more sense, because you could probably traverse that interstate from your central hub (vault 76) to rebuild, go on missions, etc. IF, and this is a big IF, if they do it right it could potentially be a lot of fun, even as a multiplayer Fallout. If it is done poorly they are going to lose a lot of respect, and fans.
More to add, I think players are unnamed vault 76 dwellers in the grand scheme of things, obviously they will pick their own name or something, which will tie in using vault 76 as the hub and make even more sense with the name of the game itself. Inviting other players via "You are invited", to reclamation day obviously, is just their cute way of having you go join your friends game under the guise of "reclaiming" the wasteland. Smart moves, and makes total sense now.
They could even have vehicles. Being only 25 years after the bombs fell the roads are probably still in a traversable state, and most of the vehicles should also be in better shape. I could see a motorcycle or something potentially. Could be cool.
Factions may or may not be player made, but I am leaning on them being player created. It will ruin my immersion, but would be nice for the multiplayer element, and a potential guild system.
Thinking more on it, I don't really see how it could actually be a Rust clone. I highly doubt the engine could handle that many players with their buildings all over the play area. Fallout 4 has a settlement limit for a reason. You have to glitch it out to make it higher (or mod it), and even when you do that it just gets more and more unstable. Low frames would be the least of your worries. It is obviously using the same engine and assets as Fallout 4. It literally looks almost exactly the same. As a consequence of using the same engine I just don't think it is plausible - at least not on the scale of Rust.