Edit - All API Apps now have access to the beta API by default. If you encounter this error it's a different issue, and you should contact Vimeo at https://vimeo.com/help/contact
It looks like you are trying to use API3.
Currently API3 is in beta, and has to be explicitly enabled by going to the url to edit your app : "developer.vimeo.com/apps/:id/edit" and add the querystring "?oauth2=enabled".
Your final URL should look like "developer.vimeo.com/apps/:id/edit?oauth2=enabled". Now save your app again with the new "OAuth 2" check box clicked and try your search request again.