The "political parts" were in the part I quoted.
From what I understand, PSG gained power because they did not join the SL efforts. They are in very good standing with UEFA.
The new salary cap/luxury tax system greatly favors them because they can easily pay the tax if they so choose.
The stuff about COVID is mostly a way not to cripple the entire football economy with FFP violations. It was needed.
The political part is mostly the Super League stuff giving PSG more influence resulting in a new system that greatly advantages them and other sugar daddy clubs (two of which were SL clubs). It does represent a shift of power as the previous system was initially implemented to prevent them from dominating the sport.
That's basically what the article implies.
The part about being able to keep Mbappé without being in violation of FFP rules because of COVID and because it is the last year of the old system so it would be surprising that a club, especially one in very good standing, gets punished.
It is all a power struggle between corrupted elites (and I'll gladly add Perez to the list of "corrupted elites").