It is actually the comitative collective of zaldrīzes ("dragon"), so literally it means "with all dragons" or "with dragonkind". Given how important dragons are to Valyrians, this usage makes a lot of sense.

Joel above has the answer. I think it's similar to how we say "bulletproof" to mean "invincible", because in our wars being bulletproof was something formidable. For them, being on par with dragons would be a metaphor for invincibility.