That means it'll work on anything. The old desktop PCs that sit around in public offices for decades will display it with no problems. Compare that to a beautiful, modern website from a rival that plain won't load let alone render on that ancient computer.
The one with the working website wins the contract.
Lots of things.
- Screen readers expect HTML tables to be tables. If there aren't things like a caption the screen reader can inform the user of a problem.
- In a lot of cases the table won't inline in to a logical structure for reading out. A screen reader will read cells out from left to right, which interleaves content from one column with content from another when that isn't the intent. CSS layout will usually read better.
- Table-based layouts use a lot more code than CSS layouts, which is more to download and more to parse.
- In the case of that website in particular, there's a ton of inline styling which is more unnecessary data to download.
- Using tables for layout makes it much harder to develop truly responsive layouts for mobile; doing things like hiding download/battery intensive page elements is much harder (especially if those things span several cells). That site does have some media queries for controlling styles, but it could be doing more.