It was Spelunky yeah. But Spelunky’s design philosophy (particularly in HD remake) isn’t very representative of most of its successors at all. It’s twitchy, erratically paced between super slow and super fast, deliberately left somewhat glitchy and poorly balanced (Derek Yu has stated that he feels leaving out some polish gives games more character and depth), and focused above all on discovering the path to a secret area by making observations across multiple playthroughs.
It stands alone as a distinctive thing not much like either traditional roguelikes or modern roguelites. (I might say that Spelunky is the Demon’s Souls of its genre.). The only other roguelite that seems particularly influenced by Spelunky itself is Nuclear Throne