WebAssembly is not a hardware ISA. It is similar to java bytecodes or .Net MSIL. The instructions in WebAssembly are meant for a virtual machine.
There is no hardware that can run WebAssembly directly. Instead, there are programs that can take WebAssembly code and generate the equivalent x86 and ARM machine code, these are called Just In Time compilers, which are core parts of virtual machines. There can be another JIT compiler for Mill machine code.
So basically WASM does not compete with Mill anymore than it competes with x86 or ARM CPUs.
If anything WASM can help the Mill. Code that is distributed in WASM format can potentially run in any platform including the Mill. This can reduce the barrier to entry for Mill adoption.
Of course, someone will have to sit down and write a WebAssembly to Mill JIT compiler.