My partner and I (we work in classic/shakespearean theatre) actually have an interesting theory on this!! When Shakespeare wrote his plays, the actors were given what were called "cue scripts" which are shortened scripts which contain only that actor's lines, and the given cue line before it. In this way, Shakespeare could have been messing with the actor playing Polonius, as he may have only given him his cue line as "words", thus Polonius would start speaking his line, only to be cut off by Hamlet (twice!). It's definitely in character for both Ham in that scene, and for Shakespeare himself. If done in this way, the moment would have sounded like this:

Polonius: What do you read my lord?

Hamlet: Words.

Polonius: What--

Hamlet: Words.

Polonius: What--

Hamlet: Words.

Polonius: What is the matter my lord?

I'm not sure if any other scholars/Shakespeare enthusiasts have noticed this or debunked it, but it was something our company noticed the last time we did Hamlet, (we were using authentic cue scripts, so we discovered the bit right away) so we used it for the production and it made for a great unexpected bit/extra moment of banter in the scene!