If it's anything like my own cartographic efforts, it works on polygons (I find that wikipedia .svg maps with the necessary boundaries as vector information are a useful source of the necessary raw data), identifies all border dependencies
1 and tri/quad/etc zone meeting points
2 that join them and sole-edge (uncomplicated coastline borders) and then after calculating the current areas of the polygons and the (relative) desired areas, performs an iterative bulging and concaving formula
3 on the border-line, then looks again at the newly, slightly shifted areas and goes round again with more distortions until it's close to that desired.
Enclaves and exclaves complicate matters, as do territories (such as Scottish islands forming their own combined constituency) that are effectively exclaves of themselves across water-bodies, so a bit of intelligent partitioning of intermediate spaces into a 'deforms around the other bits' way is useful.
You can set off-territory (sea and ocean areas) is having maximal, minimal, neutral or disinterested 'pressure', according to desired implementation. The "world nukes" map obviously just shuffles most of the land-areas down, due to the data tending to be (near-)zero in most places, but might be considered to have given oceans "positive pressure", of maybe a token single nuke to allow the properly nuclear nations to inflate out. The Falklands (
not defined as an exclave of the UK, if the colour has anything to do with it) and Antartica (probably deliberately left undistorted beyond original map projection) seem to be excluded from the algorithm for reasons of practicality.
But it's fun to mess with the data. You can even operate upon the data as if on a spherical surface but continue to render the thus-shifted information in an approximation of the planar projection of your choice. I prefer gnomonic.
1 Identical stretches shared between two polygons, probably in reverse to each other, with a bit of manual checking/rejigging to ensure two 'identical' but differently defined borders (not covered by footnote 2) are proberly harmonised.
2 Or departure points at coastlines/estuaries/inland lakes of sufficient size, which often adds some complexity that I deal with by creating a 'virtual territory' to fill in the water space and buffer it against untoward degrees of liminal distortion.
3 I start with the (non-coastal) multi-meeting points and ask that to move on a vector that's a fraction of the current 'imbalance' of the three+ areas that meet at that point, from which I then adjust the border-sides that meet there (with 'collision detection', especially concentrated near each end gpoint to ensure no over-intersection of adjacent boundaries) to reflect the current:desired area differential.