I have shared hosting account which support web deploy. I'm able to import publish profile into Visual Studio project and I can do web deploy through Visual Studio.
As Visual Studio Team Service Deploy also support web deploy to azure web app. Is there anyway we can do web deploy to website other than azure?
If the target server is on the public internet and you are using WebDeploy for the deployment it should just work. You will need to provide the appropriate authentication details in the profile (username/password or cert). Did you try this and get an error?
If the target is not on the public internet you can also install the VSOAgent within the private network and configure with VSTS. Then you can deploy to a private network.
