Formatting web pages for various displays

First I want to say that my only interest in the technical details of web development are from an end user perspective. I usually go to this site to get my weather forecasts. Their current display format is to present the forecasts horizontally but it will likely be changing soon to vertical. My two most visited pages are the hourly and seven day forecasts. It's always annoyed me that on my display (16x9 laptop) most of the space is wasted. On the seven day page it doesn't matter, but on the hourly page it could easily display twelve hours or more of data.

But when the switch is made to the vertical format the hourly page will show only five hours of data with pointless "content continues below" page breaks. The seven day forecast shows only one day per screen. It seems to me that if you are planning, for example, a multi-day activity (perhaps a trip to the beach/cottage) it makes for easier planning to see multiple days (the more the better) on one page. For single-day events, perhaps a trip to the park, seeing more hours at once is much better than fewer.

My question (and I do have one) is, how difficult is it for the web site to customize the html for the target device? I realize that many more people would access this site on a smart phone than a desktop/laptop computer, but shouldn't major sites like this try to please both smart phone users as well as dinosaurs?