Native speakers, tell me, isn't this statement true?
The meaning of "as" appearing here is no clear-cut; it contains both "at the same time" and "because."
I would say it is ambiguous. It could mean either "while at the same time" or "because", and these are not synonymous.
The "while" meaning would mean
Recent economic hardship has given the consumer increased power in Europe
and at the same time it has meant that retailers fight to win their share of reduced disposable income.
while the "because" meaning would mean that the increased consumer power was a direct result of the retailers fight rather than from the recent economic hardship.
In this case I think that the difference is not that great between the two interpretations, though.