I think you need to look beyond "my club is bigger than yours" to get anything out of those stats. But when you do you can get some interesting info out of them.
Crowds - they've given each club a ranking for the average attendance this season, and then a ranking for each clubs record attendance. By combining the two rankings they've determined a ranking for each club. So as an example, Hull may have a lower attendance than West Ham or Southampton this season they have a higher record attendance so are ranked higher.
Personally think thats a bit of a pointless exercise particularly when historic attendance statistics are available. I'd just determine the average attendance for each team over time and rank each team accordingly.
Global fanbase - there isn't a lot more you can do than things like twitter/facebook. Maybe you could look at things like TV viewing audiences but that can vary depending on the game, opponent and time of the game. So twitter/facebook figures are interesting, and like most I was surprised that Liverpool were so low. ADL makes a good point about foreign language accounts, I know City have around a dozen or so. The numbers can also reflect the quality of the content provided, so maybe if Liverpool were still lagging after adding in their foreign language accounts that might indicate that their twitter/facebook content needs improving rather than their global fanbase diminishing.
I wouldn't underestimate Chelsea's global fanbase either, it's pretty huge and growing.
Trophies - It is what it is. You can argue all day about what trophies should be included and what weighting should be given for each. Personally if I was putting something like this together I would include the charity/community shield (with a low weighting) and probably semi-final/final appearances and runner up/3rd placings as well.
Average league finish - seems pretty straightforward
Player quality - Keane, Henry, Vieira, Bergkamp, Giggs, Ronaldo, Cantona. All named in the Telegraphs top 10 players in premier league history. None count for anything by this metric. Joey Barton, Carl Jenkinson, Frazier Campbell, John Flanagan, Steven Caulker, Jay Rodriguez, Matt Jarvis all count for something. Enough said.
Pretty hard to quantify player quality, personally I'd scrap it and just go with average league position. Surely thats a better assessment of the quality of a team.
Income - pretty straightforward