In most GOTMs, the real strength... at least the full exercise of the potential strength... is not normally possible. One can only really exercise one or two dimensions of it, and so that's probably what some think a PD is.
At Diety, given an even start with a human playing PD, the AI will be no match militarily and in terms of science, and hence a player will never see or get to use the military side of PD. When a mid or late game non-PD human who is having a relatively "even" match with the AI(s) militarily takes the 10 or so turn transition, then swicth to PD, you can overcome the AI very quickly and develop technology mismatches, like vet fighters against musketeers, artillary on RR against legions, howies vs. anything, etc. Then the fun is in keeping thePD growing, but allocating a certain part of your resources to the direct military machine, while "setting up" the AI to play into your hands to get the Senate on your side, or go around the Senate (e.g., getting the AI to backstab you, or declare war on you).
But in terms of GOTMs, where a player knows about and intends to zoom up the tech tree and get those mismatches so early, then there is little serious military aspect. One could even say that a PD pretty much eliminates the need for nukes (in game terms), which is good because nukes only slow a PD due to engineer wasted man-days for repair and cleanup. One could even make a Civ 2 PD analogy to America and the wars it has fought since WWII... it diverts little resources to war (compared to economy and growth), fights with minimal "high tech" gear in most cases, has difficulty with citizens at home when the troops are away... but if it wanted to, could declare martial law and utterly flatten & annhilate & kill everything that moved in any given battlefiled, region, and almost any nation (albeit at great cost).
So what is left in a GOTM PD is mainly the expansion & growth aspect, balanced sometimes with extra science. Since the absolute score of Civ 2 is unsuitable for realistic monthly play (takes absurd amonts of real time) as we found out in the early days of GOTMs (Everyone would simply want to max out their score in 2020), the speed element in GOTM scoring is used. This then put an emphasis on efficiency (micromanagement) and in some ways 'elegance' (city layout, long term planning, when is when to end, etc.).
Since population is the biggest contributer to Civ 2 scoring, then ways to maximize that aspect are important... and PD seems to have the most advantages there.
I imagine the psychology of Demo players you ask about depends at least partly on what their state of PD grasp & application. A person new to PD would likely simply get excited to see it start working for the first time in a game they were playing, and then spend time looking at and pondering if its really true that payins shield support for every unit outwieghs a big city... or if a big city is such a good idea with all the pollution (so how do I pay for the MT/RP to remove it [Freight]). A person who can play PD, but knows it can go even better, then looks for ways to accelerate it. Those that can take most any game and get into a PD efficiently (and there seem to be a lot of those kinds of players now!!) will look to refining their play and the details, and what-balanced-against-what gives the best return, for their real-time play. That is I think what Duke and I and I'm sure others run into.
Its good to realize that PD is just one aspect of Civ 2; I think its actually the most fun in playing things like the WW2 scenario (like being Germans, in a PD, hehe). But there are lots of other strategies in Civ 2 that do not have as their goal ultimate strength and innsurmountable power, like OCC... Size 4 OCC... Early Landing... Early Conquer... even goals (in scenarios).
The most serious downside to a GOTM PD is the late-game building. In private play (not GOTM), myself and others usually quit somewhere around the Hoover Dam (on a random map), and just talk about aspects of the game along the way... no scoring, etc. But any comparison game, be it and OCC, or GOTM, or Solo's EL have some sort of underlying goal. Interestingly, a long time ago somewhere, I remember even suggesting (in the very early days of GOTMs) that population might be removed from a scoring method; in the end, the square root was used to mimimize the effect of mushrooming population, and discourage thoughts of food freight/FCT (so tedious, especially if you have tried it or seen that 26,000 ex-HoF game of Shadowdale) being used to obtain high population points. I've also suggested things like a cutoff year (or game turn) as a possibility of reducing end-game tedium... but there are side-effects of any given alteration, too.
So Civ 2 is Civ 2... and power comes from the people, and more people = more power, and more score... and so how to get that... the PD seems to still be the most efficient way to get that power/people/points quickly, even after 5 years. Hopefully players doing PD can adapt it to more "mainline" private play, where you simply want to rule your world, and do it with power, and not be accountable for little things like mistakes in micromanagement (the GOTM score is a harsh taskmaster).
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Funny you should ask! I have probably spent more time thinking about chess than Civ2 [I am a Life Master]. A chess game usually ends, by resignation, when the outcome becomes clear. So, yes - while the game is still undecided, a chess player should certainly think about it. Other activities - like running a marathon - may be difficult, but may not require much thought. So, I was wondering whether late-game civ2 is more like a chess game, or a marathon. 
