Are there LEGO plates without the word "LEGO" on the studs?
What you are seeing is actually the result of poor lighting, somewhat worn bricks, probably camera app noise reduction, and perhaps image compression, although if you look really closely you can kinda see it's a little darker where the lettering is.

As the creator, I promise that every piece in the hat is 100% genuine LEGO pieces (no knockoff brands). Unfortunately, when I took the picture the sun had set, and all I had was some weaker household lighting.

Here's another shot of the front with the face turned towards the lighting, so the lettering will catch some contrast.



The 2x2 plate in the bottom left does have more-pronounced lettering than the older 2x10 plate next to it, which is why you are able to see it better in the other picture.



To answer the question of are there plates that don't have "LEGO" stamped on the stud, no there are not to my knowledge. Even the the first LEGO plates have the stamp. Some special plates do have hollow studs though.