They did not use blue screen but they did you "mats". These were hand painted but worked EXACTLY like a blue screen. It was common to shoot way a old western movie on a set in Los Angeles and then later drop in a better distant horizon and sky. If the camera was not moving tis not not horribly expensive. A mat artist would paint an outline of the set in black on clear and this mask (or mat as they called it) whould be used in an optical printer to First they expose the film with an image of the sky and ground from (say) Utah or Texas not the mat keeps the ligh off the film in some places. then they rewind the film, but in a negative of the mat and expose the image from the set. Star Trek used this same method for their video displays. It's cheapIF (only if) you can use one mat for the entire shot. If the camera moves then you need a custom mat painted by hand for each frame at 24 frames per second.
you can NOT film a projected image. The problem is that a projector only illuminates the screen in short flashes and would have to be in exact sync with camera's shutter.
I've watched mat artists work. They project a still from the film into an easel that is about 3 feet wide and very carefully ink in the mask. It takes hours to make one and it would be nuts to make a moving mat shoot although they did do this but it's like making a hand drawn animation by hand inking every frame, You'd need to employ an "army" of artists.
Green screens are simply a faster why to make a mat, nothing new, just lower cost. but hey have been doing this for decades, going way back to the beginning of the film industry
The process you're talking about is called an "in-camera matte", and is generally used for foreground and background compositing, where the background is matted out and replaced by something else.
You basically place a piece of opaque glass (the matte) in front of the lens, completely blocking the thing you want to matte out (in this case, it would be the tablet screen), shoot the scene normally, then you INVERT the matte and reshoot using the same film, but this time you shoot whatever you wanted to put within the original matte.
I know for a fact they used film projection for 2001, the entire Ape sequence at the start of the film used front projection screen material for the backdrop, on which they projected the desert background image. It's why the leopard's eyes shine so brightly, they're shining a projector at it.
All the video displays in 2001 are also film projection (as were all the displays in Star Trek, until they started using LCDs in Enterprise), it's really really simple and cheap to do, all you need to do is sync up the the camera shutter with the projector shutters.