Your objection to the comment was that Cuomo is not running as a Democrat. The comment didn’t say he was. It made a point about liberals, which is relevant if Cuomo is a liberal. You replied that he’s not a Democrat, but that’s not relevant since he is still a political liberal. So it’s not just an “adjective game”. It’s acknowledging that liberalism is a political ideology rather than a political party, and that the problems of liberalism extend beyond registered Democrats. It’s important globally too: liberalism is problematic everywhere, whereas the Democratic Party exists only in the USA. Whatever a politician’s party, if they subscribe to liberalism their politics are going to problematic in the ways liberalism always is.

From that Wikipedia link:

Liberalism is a political and moral philosophy based on the rights of the individual, liberty, consent of the governed, political equality, the right to private property, and equality before the law. Liberals espouse various and sometimes conflicting views depending on their understanding of these principles but generally support private property, market economies, individual rights (including civil rights and human rights), liberal democracy, secularism, rule of law, economic and political freedom, freedom of speech, freedom of the press, freedom of assembly, and freedom of religion. Liberalism is frequently cited as the dominant ideology of modern history.