First, he's probably running those OSes on a monster of a machine, relatively speaking. Stuff is snappy on my desktop too, which has a PCIe4 NVMe drive and 128 GB RAM. Chromium, which is a huge and very complex application starts up in maybe a second or less.
When you're doing old school computing today it's easy to max out the specs to a point that would be unrealistic in that time. You can put 128MB RAM into a machine when most people in the day might have had 16MB. NT4 is from 1996, and that machine is from 2000, so seems likely. I remember computers back in the day. Windows 2000 ran slowly on the hardware I had.
Second, modern software does way more in the name of convenience. Eg, nobody really uses notepad. We use VS Code for instance, which is an enormous application, the sort that would have seriously challenged a computer back then.
And really everything grew in the same manner. Discord is big, but Discord draws its own widgets and includes a web browser. If you did Discord with native widgets, plain text and without all the fancy stuff like animated emoji and special effects, it'd be much lighter and faster to start too.