How to read a missing category
Steam maintains distinct categories for online co-op, LAN co-op, and shared or split screen. A developer ticks the ones that apply, and the store shows them on the page. Dumpster Gang carries online co-op. It does not carry the other two. The Microsoft Store listing agrees from a different direction: its structured capability list has exactly two entries, “Online multiplayer (2-4)” and “Single player”.
This is weaker evidence than a developer saying the words, and stronger than a guess. Categories on unreleased games are sometimes incomplete and do get added closer to launch, so this could change. But two storefronts describing the game independently, neither mentioning same-screen play, is the strongest signal available before release.
Why people keep asking
The genre invites it. A chaotic four-player physics sandbox is exactly the thing you want to play in one room, and several of the games it is being compared to do support couch play. Wanting that from this one is reasonable, which is why an accurate answer matters more than a hopeful one.
The practical answer for now
Plan for four PCs. If you were going to buy it specifically to play in one room with one screen, that is not something anyone can currently tell you will work.
Categories read from: Steam store page (appdetails API, appid 2870790) — storefront record.
Local play questions
+Does Dumpster Gang have local co-op?
Neither storefront lists it. Steam has a dedicated shared and split screen category and this game does not carry it, while it does carry online co-op; the Microsoft Store capability list contains only "Online multiplayer (2-4)" and "Single player". No developer statement has addressed local play either way.
+Is there split screen?
Not on the current store record. Split screen would show as the shared/split screen category on Steam, and that category is absent.
+Can two people play on one PC with two controllers?
There is no information saying so. The game does list full controller support, but that describes playing with a controller rather than playing with several on one machine.
+Could local co-op be added later?
Categories can change before launch, and a game can add features after it. Nothing has been announced, so the honest position is that it is absent from the record today.