Confusing web design and desktop UI design in the 90s does little to dispute the assertion that desktop UI design peaked in the 90s. In the late 90s, the browser was completely new - so there was a lot of skeuomorphism, borrowing from other media to try to make the web work well. Space Jam's format was familiar, though to users of multimedia CD-ROM and other interactive hypermedia of the era.
The desktop application GUI - which is really what people are claiming hit the peak in the 90s, really did. Menus, windows, tabs, dialogs, scroll bars etc... all were fairly well settled, and users understood them. A user who knew Word for Windows could do pretty well using WordPerfect for Windows. Most day-to-day applications were pretty easy to figure out because discoverability was very well done, and wizards and how-to dialogs helped users through the rough bits.
There was consistency between applications - save in areas where the OS didn't really provide GUI guidance - so design, CAD, and other creative apps (hi, Adobe) often had divergent ways of doing things and came with a steep learning curve. The web took off because it actually worked a lot like the multimedia CD-ROMs that preceded it - and websites were a lot easier for developers to build.