EarthBrowser takes data from disparate sources and displays them on a 3D globe. I'm not sure what the exact definition of a "mashup" is, if there even is one. I think it is something like a service that draws together one or more sources of data and uses a mapping API to display them. Does the definition of a newly coined word like that really matter, or is it the underlying concept that is being labeled what is really important.
EarthBrowser certainly doesn't use an external mapping api, however it's internal program structure provides it's api. Are those KML files created independently by people defined as a mashup? My guess is they are not, but why not? Does a mashup require display on a web page, i.e. a web browser as a display mechanism? That seems overly restrictive. Perhaps it requires the logic being applied to the data through server scripts preparing it for final display. Google Earth with KML generally just displays static data, but it certainly can allow that through KML via a network link. Perhaps that is why so many in the geospatial community are excited about the network link in KML. It allows Google Earth to display live data, albeit in a pretty hacked up way.
I submit that the current definition of a "mashup" is a somewhat misleading goalpost for the amateur GIS community. The underlying concept of displaying location based information is much broader than what is contained in the current crop of mapping APIs. Also the restriction of server based processing of data is one that isn't an inherent restriction, there just aren't any tools to do general geoprocessing on the client side. Yet.
Update: I forgot about ArcExplorer which is supposed to have a pretty decent set of client side geoprocessing tools. That's what I get for trying to post when looking after a toddler and 6 week old...