I dont think the only apps people use are web apps. I just think that the majority of apps are moving to the web(basically, like you said, data driven applications), like CRM applications, Payroll applications, everything enterprise due to 'SOA's(Service Oriented Architectures), and more.

The web doesn't require a download, or an install like emule, kazaa, or bearshare. Web based applications also have less of a chance(if any) of infecting your computer with a virus like file sharing programs.

Gaming(imo) will always be native to the machine, only utilizing a connection for competing against other players.

So, it really doesn't become insignificant, it just takes more a back seat to applications that allow for more human interaction(any social network), profit(crm apps, soa's) or fame(myspace, youtube).