Theoretically, one could run code in vscode.dev if an extension provides a programming language runtime. I'm not sure if there are any extensions which do this yet.
It is interesting to think about how many general-purpose VM-like abstraction layers are sitting on top of each other to run this — the operating system provides an interface which the browser uses, the browser provides an interface which vscode.dev uses, vscode.dev provides an interface which an extension implementing a programming language runtime uses, and the program uses the runtime interface.
Github Codespaces has the downside that you need to connect to a cloud computer and do all your development remotely on the cloud computer, which causes issues such as lag, the need to pay money for the service, inability to use it without an internet connection, etc. This provides the benefits (however small) of a development environment running in the browser without those downsides.