I think a transpiler is a compiler that does a high-level to high-level translation with only a few simple transformations and almost no optimisations and produces relatively readable output.

If a C or Eiffel compiler meets that definition then yes. I'd still call it a compiler, but I would also call it a transpiler.

If you're offended by the term transpiler because all transpilers are also compilers, then I don't know why you wouldn't also be offended by the term compiler because all compilers are also 'programs', so lets just call everything a 'program'.