Because you can have a decent stab at predicting how a club's actions during a transfer window have affected its chances of success in the forthcoming season.
"Showing ambition" just means the prediction is that that chance has increased.
As you correctly point out, the most hyped, biggest names aren't necessarily the biggest boost to a side. But as Asa equally correctly points out, usually, they are, and in any case, the determining factor is not whether they actually are, but whether they are perceived to be by those making the prediction.
Players really want their clubs to succeed not just for emotional but also financial reasons. Not only do they earn performance-related bonuses, their valuations increase for the purposes of future contracts, and their enhanced profile increases their opportunities both during and after their playing years. Plus, they become popular and famous.
Sure, loyalty is mostly bosh and players act on mostly selfish motives, but "showing ambition" is just a metaphor for that coarse measure of a club's chance of success that a player may make. All relative to his options - when he has good alternatives as Van Persie does, it's a factor in his career decisions.
