Yep. But "cards". I honestly don't like it.
Good news then, last one is not a card game.
But i still would suggest waiting for a bit, there is not much content yet.
I cant think of any rpgs with dots. dragon age origins has quite a few dot spells, but their mostly just secondary
They definitely exist.
Granted, vast majority of examples i can currently think of are these auto battler roguelikes you can find on steam.
Tales of MajEyal has DoT builds. It's only a little indie game though, but good.
There is this Rogue posion knife thrower build and i remember having a very similar experience of killing an elite mob by placing bunch of DoTs and running away as Cultist of Entropy.
As for other games with dedicated DoT characters...
There is Path of Achra there you can build your character around applying million stacks of cold, sickness and whatnot. But everything dies so quickly(especially if you're doing things right) i doubt this is what
Cryomancer looking for.
Crystal Project has Shaman as a dedicated DoT class, if one is not allergic to JRPGs or
incredibly infuriating amount of platforming.
Soldak games, assassin spec from Din's Curse/Legacy and Zombasite definitely fits the criteria. Drox Operative games also have some DoT weapons, i think?
Chronicon might also count, probably.
There is also this dungeon crawler i can bet none of you have heard of.
Made on RPGMaker as you can see, plenty of small annoyances concerning UI, bugs, unclear information and stuff.
But i found classes you can pick are pretty interesting and some of them can definitely be made into DoT specialists. Like Ship Surgeon can be built into a DoT class, healer or a "disabler"(someone who can cut "leg","torso" or "head" which prevents enemies from using attacks associated with these body parts, also grants extra loot after battle).