Actually, Condé Nast hasn't owned reddit for a long time.
When Condé Nast originally bought reddit, there was an outcry about how Condé Nast was going to ruin reddit. People thought Condé Nast was just going to pump their magazine content (GQ, Vogue, New Yorker, Wired, many more...) on reddit.
In order to prove this wasn't going to happen, Conde Nast reincorporated Reddit as its own company and moved it under its parent holding company (Advance Publications).
Advance Publications is to Conde Nast what Alphabet is to Google.
Also one thing to note is that Reddit has employees within Conde Nast's head quarters. Its not like they are trying to hide their ownership. They just changed the structure of the ownership to prove Reddit still controls Reddit.