The laptop will not block an hdmi out because it will have no way of telling the website what screen your watching it on. The mobile phone tells everything to the app so it knows your connected via hdmi and will block it mostly because they negociated and agreed to the rights holders for these restrictions to be put in place and enforced on their mobile app.
As he said, its more about rights. That when you are paying for your TV, and get the Anyplace TV included, you are paying to watch it in your house. And in the case of anyplace TV, for you personally to watch elsewhere. (assuming that only you will be watching on your small screen). That with your payments, your paying for you to watch it, not someone else.
That with allowing to stream via other methods from the phone, etc.. makes it way to easy to technically then just plug in at any friends place, and watch stuff there. Which 'technically' isnt allowed due to those rights. Though.. this then effects being able to watch in your own home then too (but they assume you have TV boxes there).
As Pauly said, the computer they dont really have any way of knowing/monitoring in the same way. On phones there are ways of monitoring the hardware & methods of output.