Drought resistance refers to whether the plant can survive droughts. it does not necessarily refer to the plants yielding well under drought. However if the plant is still yielding, it could even become more profitable as other plants stop yielding. The deep roots of the plant help it under drought, as the Soil drys top to bottom. Plants that have deeper roots maintain access to water, while the top is already dried out.

To try a poor metaphor: Someone who is 2m tall but short-sighted will still see better in a crowd than someone who is 1.60m but has the best eyes in the world.

https://www.canr.msu.edu/news/managing_alfalfa_during_drought

Alfalfa is drought tolerant compared to other forage legumes like clover. This means that during drought the alfalfa will fare better and also yield better than clover or a grass like Timothy or blue grass. However as you can see pasture is also on that list you linked. Fodder crops are harvested for their entire biomass above ground and the amount of biomass is very large. It's a very productive crop and makes a lot of fodder and this fodder is mostly water. Therefore it takes a lot of water to grow. The water required is not extreme in any way however and where I live alfalfa is a rainfed crop that only very rarely has any water deficiency symptoms. The extreme amounts of water applied to alfalfa in the south east of the USA is only because of the desert climate there. Growing beans, corn or potatoes there also requires insane amounts of water. If potatoes were chiefly grown in the desert southeast you bet you would see news articles going around about how terrible potatoes are. In the end it's only a matter of matching the right crop to the right climate. Even the most water hungry crop on earth will not require irrigation in the most rainy place on earth.