It's funny, but at the time this was written this was kind of a controversial and insightful statement. Now, it sounds so obvious that it's a cliche. Amazing how quickly culture can change. This was written barely 10 years ago!
I remember working on sites back then that might be considered web apps, and I don't think you could even count on cookies at that time. One experiment I did involved passing data along (part of the URL in a GET, or a continuous set of pages generated via POST requests). Everything done on the server side (even Java applets were problematic: http://www.conman.org/people/spc/refs/search/search.hp1.html).
Web apps at the time were more ... um ... document centric than now. But still, despite the lack of cookies, AJAX and Javascript, databases still existed back then, and CGI programs could be written in any langauge (Perl was popular back then). So it wasn't completely hopeless, but the apps were simpler though.
In truth it wasn't so bad. Markup was more cruder and more troublesome than today with HTML4/5 and CSS2/3 but there's nothing wrong with a simple layout. Cookies couldn't be entirely depended on but you could still keep track of the equivalent with a query parameter that you put into every url. Server side tools were cruder but there was still perl so you didn't have to roll everything on your own out of C (though many web apps in 1996 were written in C/C++). Some of the biggest web companies of today such as amazon and ebay got their start in that era and were already doing big business even back then.
Assuming a crap UI is tolerable for business purposes and assuming that you wouldn't have to market it.
Back then, you wouldn't use PHP, CSS, Javascript, XMLHttpRequest or Flash. They didn't exist or hadn't matured yet.
Most likely, you would've used a Java based solution, such as NeXT WebObjects. That's what e-commerce businesses did back then. However, you wouldn't have developed the product on your own. You would've needed a team and plenty of funding, in part because WebObjects came with a $50,000 price tag.
I encourage you to read this WebObjects advertorial from april 1997, courtesy of the Wayback Machine. It's a good illustration of what was considered modern web development:
http://replay.waybackmachine.org/19970412201603/http://www.n...
WebObjects - didn't have any direct experience with that back then, but it and many other proprietary options were quite pricey, IIRC.
The DOM wasn't standard, HTML4 was still in the works. I'm not sure if IE2/3 or Netscape 2 could even dynamically access table elements at the time.
Javascript performance was utterly terrible, and JScript had a strong presence that created an important and problematic language/support divide.
CSS didn't exist at all, your visual styles were either images or elements rendered as the browser saw fit.
XHR didn't exist and wouldn't exist until IE5, 4 years later. There was no way to update a page without a round trip to the server. This was also during the days of AOL and Dialup.
Ugly as sin? Slow as hell? Absolutely. Probably doable, though.