This is just google trying to make sense of nonsense Japanese; the Xのこと is something like 'X's characteristics' (sounds really stiff, but that's how i'd concis

This is just google trying to make sense of nonsense Japanese; the Xのこと is something like 'X's characteristics' (sounds really stiff, but that's how i'd concisely explain it) so のごとが好きです is like "i like 's characteristics" and is semantically meaningless.