Because Republicans who use "Democrat party" think they are being clever and funny, but it just sounds weird. They are the same ones who say the US is "not a democracy, it's a republic" as well.

For whatever reason, they hate the word "democracy." Wonder why?

Every elected Republican does this now. Good thread on it here, it goes back a long way.
https://www.dcurbanmom.com/jforum/posts/list/824882.page

Same reason they pronounce Kamala incorrectly.

They are weird and embarrassing.