I'd define "web application" as "something that lets you perform a task via the web". All of the companies I linked count under that definition; Amazon let you buy books; EBay let you buy & sell odds & ends; GeoCities let you build a website; WebCrawler let you search for things.
If you define it more narrowly as "something that lets you create a site", Geocities still counts.
I think you'd have to narrow the category to "first online store builder" to make it accurate, which is still quite an accomplishment, but certainly isn't the "first web app".