First time i have tried to use tv anywhere and after all the messing with registering the device using the primary user since that it a thing...finally got it sorted and tried to click on the BT Sport 1 and like you it says i am using an android device and need to download the app.
Sorry to hear that you're unable to watch BT Sport through your laptop.
If you are using Internet Explorer are you able to check if the version is between 9 to 11 or if the browser is Firefox it needs to be 3 or higher. Google Chrome is not supported for TV Anywhere.
If this is still not working, as you have one device change available, you can sign into your account, under My Profile on the right hand side select Device Settings and remove the device. Once the device is removed, re-register the device then try to stream a channel.