Yes. You need an Xbox Live account no matter what to play other Xbox players online.
You will play all your games on your Xbox as you are used to doing. You login to Rival using an internet-connected device, like a computer, a tablet, a phone, etc. You can use the rivalgames.com website, or the Rival App downloaded to your phone or tablet. Rival allows you to make the most of your existing Xbox and Xbox games by competing in tournaments and events!