Yes, you can win them in the slots. It's how old timers got them. In the beginning, the game was bugged and people could win mark cards. Nowadays they're an option as a prize for winning a tournament. That's how I got mine (mark of time).
The person you were playing was Stymie, I'm guessing (she's the only one I know of who has a mark of fire). She was one of the few who got one when the game came out.
(Edit: Didn't look at whole image. Guess it was Jumba >_>)
Unupgraded, they act like pillars and if your mark is the same as them they stack with it (giving you a 2x mark). Upgraded, they just act like normal towers.