For example, an American who apologizes for the wealth and power of the United States?
Not an exact term for the people, but, as described in the Urban Dictionary, they are suffering from an embarrassment of riches.
an overabundance of something, or too much of a good thing, that originated in 1738 as John Ozell's translation of a French play, L'Embarras des richesses (1726)
I think that the sense of guilt you are probably referring to has generated many rich philantropists over time and with that respect the term can also cover you definition:
a person who shows altruistic concern for human beings, esp. as manifested by donations of money, property.
For a society that has fed, clothed, housed, cared for, informed, entertained, and otherwise enriched more people at higher levels than any in the history of the planet, there sure is a lot of groundless guilt in America. Manifestations of that guilt abound. The example that peeves me the most is the one we often hear from well-meaning philanthropists who adorn their charitable giving with this little chestnut: “I want to give something back.” It always sounds as though they’re apologizing for having been successful.
I have worked with top athletes in a few sports and there is something that in the coaching circle that we use to describe the phenomenon of an athlete feeling guilty for their own or team's success - winner's guilt.
This is the guilt by being associated with winning or being extremely "better". When training these athletes we have to deprogram them because they are so used to toning down their game that not only do they perform worse with worse competition but they also perform worse when good competition is performing poorly.
I have heard the term winner's guilt associated with sports and lottery winners and I am sure it fits your context (at least somewhat).
Survivor guilt is often used to describe someone feeling guilty about winning, or outperforming someone else. It is most pronounced when someone out-performs a family member or close friend, although it may also be used in reference to feeling bad about outdoing a stranger.
While we all think consciously that we want "to win" in fact we are wired to prefer equity, and there is a downside to winning, that is feelings of survivor guilt. For example when an industry is going through lay-offs, and one worker is promoted while his/her friends, family members, colleagues are let go, the remaining employee often suffers from survivor guilt, which is usually just under the surface of conscious awareness.