Yes, you can only do this if you have a fixed-size screen, an orthographic camera, and an exactly known sprite size / texture resolution.
For anything where you want to change screen resolution, you have to either author one sprite image for each resolution, or design sprites that work well when blended/scaled.
This is typically done inside the art tool. Reading about your art path, I wonder if there is a way to generate anti-aliased paths when importing from Illustrator in Photoshop?
Also, when you say it looks good in Photoshop, is that at the resolution you’re showing on screen in game, or at some larger resolution?
In general, I would advocate against using Nearest filtering – it will cause blocky-looking outlines, and often also causes “flying pixels syndrome” on moving objects that aren’t just flat colors.
I actually think your clouds have this lack-of-alpha problem, too, because the edges around the rounding look a bit blocky. The reason they look better than blue guy is that the blue buy has a much thinner black outline. If you aim for all lines to be at least two pixels wide on screen in the game (at your desired resolution,) this will probably be easier to manage.