SketchUp Shop is a web based version of SketchUp. Just like SketchUp Free, it runs on your browser. Your Shop subscription unleashes features that the Free version has not (import and export/styles managing…)
You can acces 3Dwarehouse models through the component tab on the right.
Ignore the message, when you want to continue the browser based version that you allready have.
Probably you downloaded the desktop version, the subscription to your Shop version does not include the use of the Desktop version. By double clicking on the preview image, it opens in the desktop version.
If you download SketchUp models via the browser to your download folder (not directly from within the running Shop version) you can upload them to your trimble connect folder and open them in SketchUp Shop.
Note that any desktop version has a (release) year appended. (Ie. SketchUp Make 2015, SketchUp Pro 2017 etc.)
The web based versions of Sketchup do not need a year, they get updates all the time.
If you want to use the desktop version you would have to buy the Pro license, which are perpetual, you cannot upgrade the Shop subscription since they are different products.