Chelsea shouldn't be lumped in with City and PSG because they are not a state owned club. How much they spend has no relevance to it. Chelsea are merely the more competent and long term English version of 80s and 90s Italian clubs like Milan , Inter, Lazio, Parma all of whom spent a shitton and bought top players in a bid to become successful. This model wasn't alien to England either as Blackburn had won their PL due to massive funding and more recently clubs like Leicester, Villa, Wolves etc have all followed a similar pattern. The difference between Chelsea and these clubs lies in the fact that Chelsea spent a lot when the transfer market was going through a low in the mid 2000s after the early 2000s bubble and thereby made more of their investments enough to propel them to the top in the long term. Its still very different from being funded by a state as there is an order of magnitude difference between the spending power of a billionaire and an oil state.