It's virtually impossible to make a website that is well designed on both desktop and mobile. As long as the affordances of mouse+keyboard and touchscreen are as different as they are, one of the user groups needs will suffer a detrimental compromise.
After that, what you can do is ruin it, targetting a webpage for a specific screen size.
A phone screen just isn't big enough to display tables with more than two or three columns. There's no reason desktop users should need to be crippled in this fashion.
Tables are a very powerful tool for conveying lots of structured data in a way that's useful and intuitive. Avoiding them means losing out on this.
This is the exact problem the website we're discussing is having. You just can't show the relatively small amount of information side-by-side on mobile the way they are trying to. The only solution to it is to make it less intuitive and show them on top of each other in a complete jumble.