Hi jojo1224
Sorry my French is not the best so I hope you can English or at least translate it properly.
Based on your statements I assume you logged on WebTV with option "Natel-Login" (or if you created it in the customer center the second option "Swisscom Login"). Note that "Natel-Login" IS NOT the same as the "Infinity-Login"! If you compare the login between App and WebTV you'll see that on the App you have the option for "Infinity-Login" whereas on WebTV you don't have it (yet). This means the TV Air promotion for 12 months with TV 2.0 Basic is limited to mobile devices with an Infinity abonnement, resp. the App only.
If you login with the "Natel-Login" to the WebTV you'll get a TV 2.0 Light account which is completely separated from your Infinity account. TV 2.0 Light means less channels to watch and no Replay/Recording options, basically just Live-TV. Rai Sport is obviously just available with TV 2.0 Basic or Plus. That's why you can't play them over the "Natel-Login" over WebTV.