The answer is no, you don't need to purchase again.
If you purchased the option to remove ads in the Google Play Store version of Torrent and later you want to use the website version of   Torrent Pro, you don't need to make any purchase again. This is because both our Play Store and website versions use the same signature, so the same option will be activated here. You don't need to purchase again.
But remember, whatever email ID you used to download the Torrent app from the Play Store, that email ID will be linked to the purchase you made. So when you install the app from our official website https://torrentpro.qinfro.com, make sure the same email is set as default in the Play Store, even though you are not installing from there.