There is result of my research of score calculation:

Update 4.9.2019

population any type: +3 points each
hero level: +2 points
quest: + 4 points
tech first level: +4 points
tech second level: +6 points
tech third level: +8 points
tech 4th level: +10 points

tech 5th level: +12 points

tech 6th level: +16 points (not 100% sure)
new system: +12 points
system level upgrade: +6 points
won battle: +2 points
laws: +3 points
assimilated minor system: +5 points
wonders: +20 points

war won: +5 points

Described in xml file but gives no points:

trading company: +7 points (doesn’t work)
trading company level: +5 points (doesn’t work)


System improvements, planets, ships and trade don’t generate points so far.

When you start you have normally 34 points: 1 system, 1 law, 1 hero level, 3 population, 2 techs first level.

The points for trading don't work now and i asume it could be a bug because the tooltip and xml file mention this type of points generation. 

Thanks! How does it work for laws, then?

Nevermind, it counts laws active. I thought score system is cumulative, but it is purely additive. Really strange, because as you've said, nothing apart population, system count and research meaningfully affect your score. "Go tall" my ass, this game is designed to play wide.