Denisty should refer to exactly that - how much a given volume of something weighs. IE: Petrol is less dense than water is less dense than mercury.
But many people say 'density' to talk about 'energy density' when it comes to fuel.
This relates to how much bang you get out of a given volume.
For example, methanol has a lot of things going for it, but is quite poor in terms of energy density - you'll probably pour twice as much into the engine to make 25% more power
(these are made-up figures, don't sweat their accuracy).A lot of the 98 octane fuels are mildly oxygenated - this means that they contain some oxygen within them, that is released as the fuel burns.
Nitromethane is a highly oxygenated fuel - when it burns in an engine, it releases more oxygen into the combustion chamber. So you run a very rich mixture as a fair bit of the oxygen required for combusion is brought into the engine by the liquid fuel.
Obviously this requires less air (which takes up a lot of physical room) to give a bigger bang - so you get more HP (everything else being equal).
WRT harping on about "98 octane fuels" you're right - the octane rating is almost irrelevant if the engine isn't pinging... But in the world of simplistic mass marketing, it's the "high octane" fuels that get all the good stuff. In other words: the octane rating is only one of it's attributes, but it's one that's does have some advantages, is easily sold to the punters, and the punters think they understand.
It's like comparing a YZ to a DT and only talking about how much power they make - the YZ is faster around an MX track because it does
everything better, but it's easiest to say "Look at that! The YZ125 makes twice as much power as the DT! Bet she honks! Hooooeee!".
PS: I love NGKs - never had an issue with them, but have had dramas with other brands. Go figure.