Hi Adam,
The deployment utility is a tool only for updating only the Windows Operations Dashboard, it doesn't update the browser Operations Dashboard. Instead, the browser Dashboard is rolled out with ArcGIS Portal i.e. when you install or update you Portal, you automatically receive the latest version of the browser Dashboard and you don't need any additional deployment like you do for the Windows app.
For your second question "or is there no new version?": At this point we don't have any planned release for the browser Dashboard. Our team is in full speed building the next generation Operations Dashboard, it is also a web application and will eventually replace the existing Windows and browser Dashboard. We encourage you to sign up for our Beta program (http://www.esri.com/products/dashboard)) to give it a try and let us know your feedback and what features you want to have in the next gen. Dashboard.
If you have more questions please let us know,
Tif
