I think people get too worked up over "Spell Slots". They're just a mechanic, a means by which the character can do something. They don't mean "magical power". or at least, they don't have to. "Spells" and "Spell Slots" are a way of giving a variety of options for things to do in a given situation, and a limit on how to do them, without writing out a special mechanic just for this class to do the same. The pdf even says as much in the sidebar. You wanna cure someone, but don't want to be channeling "Divine magic"? Sure, you have a salve you can put on them that you've been working on. You want to cast "Disguise Self", but with no magic? Sure, you figured out how to do a hologram on yourself, either through advanced tech or Rune Magic or something similar.
This way, there's a huge list of effects they can do (spells) but a limit on how many times they can do them (spell slots). It's naturally upgraded as the character levels, it's on par with other classes in the progression, and most importantly, they don't have to recreate the wheel to give you "something unique". If you don't like spell slots, don't call them spell slots. Call them Artificer Slots or Gadget Uses or something like that, that just so happen to have the same functionality as Spell Slots.