Of course it is!! Doom has been ported to a lot of platforms, even very weird ones or even not intended to run it at all! Second, DOOM modding community is amazing. A lot of quality MAPs, MODs.
And as bonus :) I still play good old DOOM using source port. Okey, enough talking, time to fry some monsters :)
cult classic is defined as "something such as a movie or book that is considered to be one of the best of its kind by a small group of people." which I would say is pretty accurate
Doom had over 20 million players in 2 years. That's higher than some modern games. I don't know if something groundbreaking and gigantic like that can ever really be 'cult'.