The translation of 贅沢 as luxury is not wide off the mark, but it's not accurate either. Sad to say, that's what you get from a Japanese-English dictionary.
If you look it up in a Japanese dictionary, say, the default dictionary provided by Mac OSX (スーパー大辞林), you get different meanings. The first one of them is "必要以上の金や物を使うこと（さま）", things like using money or good that is more than necessary. I think this meaning would fit to the context mentioned above. The second meaning given by the dictionary indeed corresponds to the English luxury, "金・労力などを多くかけていること（さま）". You may need to consider the context to determine which sense is used.