That's a linguistic not economic definition.

"In economics, utility is the satisfaction or benefit derived by consuming a product. The marginal utility of a good or service describes how much pleasure or satisfaction is gained by consumers as a result of the increase or decrease in consumption by one unit."

The definition you provided still doesn't give a proper method of classification of what a luxury good is.

Here is what you're probably looking for:

"In economics, a luxury good (or upmarket good) is a good for which demand increases more than what is proportional as income rises, so that expenditures on the good become a greater proportion of overall spending."

TLDR: in other words, in a desert full of diamonds, water is a luxury good, while in a city full of water, diamonds are a luxury good.