I think you're misinterpreting it. Watch that clip again. The "tablet" Bowman puts down on the table is noticeably larger than the screen Poole is watching and is white edge-to-edge (suggesting a paper surface.) Bowman is putting down some kind of clipboard or file, not a tablet. When we rejoin Poole at the table after getting his meal, it's implied that he has put away the file/clipboard and has activated his screen.
I'm saying this based on what I know of the book. In the book, the astronauts keep in touch with Earth news via computer screens built in to the desks. (On a side note, it's sort of amusing when you read it, because Arthur C. Clarke accurately predicted that people would be able to read the world's newspapers on such a system, but he describes it in a pre-point-and-click world where the astronauts are typing a number to go to a given newspaper.)