The problem here is that the bits of information needs to be clearly defined, otherwise we are not talking about actually quantifiable information

here they are talking about very different types of bits

I think everyone agrees on the definition of a bit (a binary two-value variable), but the active area of debate is which pieces of information actually matter. If information can be losslessly compressed into smaller representations of that same information, then the smaller compressed size represents the informational complexity in bits.

The paper itself describes the information that can be recorded but ultimately discarded as not relevant: for typing, the forcefulness of each key press or duration of each key press don't matter (but that exact same data might matter for analyzing someone playing the piano). So in terms of complexity theory, they've settled on 5 bits per English word and just refer to other prior papers that have attempted to quantify the information complexity of English.