Haha...
I dunno what it's like for everyone else but I usually have my laptop next to me whenever I watch a movie or a show on TV. If what I'm watching is engaging enough I won't look at the laptop at all. To me that's taut drama. It is engaging, you feel like you need to take in every word each actor is saying, it is just that important. True Detective, Broadchurch, Game of Thrones, Black Mirror, Sherlock,... these shows to me fit that description.
If the opposite is true, I'll be surfing the net, reading Jazzfanz, checking out ESPN, etc, while peeking at the show/movie once in a while to make sure I know what's roughly going on. If I have time to do all that then it's not engaging enough for me.