Based on the RPG, Damiel's spells should be no more one-shot than Ezren's. They are essentially the same type of "casters" with both of them having "spellbooks" and preparing "spells" at the start of the day or leaving preparation slots open to prepare what is needed when a situation arises. The only difference (and the reason for excessive "quotations") is that Damiel isn't technically a caster, his spellbook is called a formula book, and his spells take the form of potions. Otherwise, his extracts/infusions act exactly as spells do (including being affected by dispel magic) and he can prepare them for free at the beginning of the day just like a wizard can, day after day.
For him to not have the chance to recharge spells would be, in my option, a misrepresentation of his abilities. I feel that the developers are being very careful about how this issue is treated, evident by the fact that this thread hasn't been answered yet even though we have been assured that it is being discussed and we should wait for a ruling.
I still feel that the intent of the wording is considering the "step" being the entire process of the spell resolving, meaning it's entire Power text, so even if it is a display spell he'd still be able to recharge it. However, this would be problematic because it says he "gains" the skills. He could then play a display spell that lasts until the end of the turn and play Attack spells safely on a later encounter which definitely wouldn't be the intent. I think the ability really needs to have an elegant re-write to work. Once I get my Add-On Deck I'll be playing this as I feel it is intended. Since he isn't OP legal right now, I'm okay with doing that for now, but it would be nice to get the official word on it.