AirPlay a DVD via a MacBook Pro to a TV problem

I wish to AirPlay a DVD via Apple TV to may large 42" TV. The MacBook Pro I have is a mid 2010 17" Model running OS 10.11 (El Capitan) which doesn't have the AirPlay function (it's too old).

I downloaded a third party application called AirParrot 2 which apparently has the same functions as Apple's AirPlay. I can bring up on my MacBook Pro's desktop and on the TV and do all other computer functions. It displays (mirrors) what's on the MacBook screen. If I insert a DVD whether its a commercial one or one made by myself using iMovie all I get on the MacBook is a grey screen and similar on the TV.

I borrowed a friends MacBook Pro that does have the AirPlay function and the DVDs will not display either — just the grey screen comes up.

Is this whats suppose to happen or is there something else I need so I can AirPlay a DVD to the TV?

Advice appreciated. Paul L'Huillier (Australia)