WASM is an abbreviation for WebAssembly. If it doesn't have DOM access, WebAssembly is as related to the Web as JavaScript is to Java. A language ecosystem with no I/O capability is as much use as a one-legged man at an arse-kicking party.
Well, arguably the worst thing about WASM is the naming.
It's neither directly related to the web, nor is it an assembly syntax.
It's just another virtual ISA. "Direct DOM access for WASM" makes about as much sense as "direct C++ stdlib access for the x86 instruction set" - none ;)
WASM is to webbrowsers what WebGPU is to webbrowsers. Designed with browsers in mind, but not bound to them.