Progression is in the players skill itself. I like to think of roguelikes like a competitive online RTS or MOBA. The first few games you get absolutely rocked by more skilled players but you gradually improve your own skill, learn tricks and counters to unusual situations and you slowly get better and better. I don't think there's a need to carry over character stats or equipment between runs. This is not supposed to be an RPG though obviously there are some similarities.
Hello, please see my answer to UNKNOWN0DARKNESS.