Disclaimer - I'm not very familiar with the specifics of the 737NG (or any 737 model for that matter). But this is how it works on other Boeing models with EICAS:
In Normal mode, the EEC will protect the max N1 (or EPR) rating for the ambient conditions (with a little 'head room' to account for air data sensor differences). Without some sort of failure, it's not possible to significantly overboost the engine in Normal mode.
In Alternate mode, thrust rating protection is lost - it IS possible to overboost the engine - by a rather large amount (again, depending on the ambient conditions). The EEC will still protect N1 (and N2) redlines, so without some sort of secondary failure you can't exceed rotor speed redlines (EGT is a different matter). This introduces a risk that a pilot may have a brain fade - forgetting that they are in Alternate mode - and advance the thrust levers full forward resulting in a massive overboost. On EICAS equipped Boeings, there is a Alert level message that will come up (aural alert and text) if N1 Command is set 2% (or more) above the Max N1 as computed by the aircraft (FMC or FMC type function).
What I'm guessing is that - on the NG - lacking EICAS, they can't put up the message, so they simply turn the N1 gauge red.
But that's just an educated guess...