No, it's an interpreter for CIL. Wine is mostly an implementation of the Windows API, not an interpreter or emulator of any kind.
They say it has a JIT, a just-in-time translator. Not an interpreter. Wine also has a translator that translates Windows application's calls to Win32 into calls to Linux API.
The comparison with Wine is not totally incorrect.
I think it's normal to include a JIT as a specialised form of interpreter.
CoreCLR, the .NET Core runtime, does not have an interpreter - it JIT compiles the bytecode immediately. Given Mobius is a .NET inspired project, it’s likely it will follow that approach as well.
JIT is a compiler - bytecode to native code. Wine is not a translator in that sense - it doesn't rewrite native code to change the APIs it calls. It just provides an implementation of those APIs, which may (or may not) ultimately invoke some POSIX or X API.
It might be an interesting perspective to think of almost any software library or framework as a kind of interpreter or translator from the layer above it to the layer below - e.g., a web browser is a translator from DOM constructs to native draw calls?