Because it’s the only other thing about that system at all. OP wasn’t teaching, just showing what that system does. If you looked for a source that explains it you’d be told

I think the “rogue” in rogue-like refers to the fact that you start over if you die. Not the similarity to the actual game. Am I misunderstanding you?

I think I get what you’re saying, that rogue-like was named after the game and therefore this genre should be named after slay the spire. But I think Rogue named the genre because there wasn’t anything else like it. Slay the Spire is still at the end of the day a mashup of two existing genres.

I really think it deserves its own genre. Games like Cobalt Core, Balatro, Tower Tactics Liberation, Alina of the Arena and Loop Hero are all unique in their own right and differ greatly in gameplay from Slay the Spire and each other but still hold to the deck building rogue-like core.

Slay the spire is the granddaddy of the genre, but isn’t the single defining example by far.