This argument is too generic because it's asking if it's it's ok to judge a game if you allowed yourself to be distracted by something. It implies all games have the same purpose. Games are a medium like books, TV/Film, paintings, etc. They can be practical, light, deep, oppressive, inspiring. Can I judge a magazine article I'm reading if I read it while the TV is on? If I put on some epic beloved film for my partner to watch and she's constantly looking at her phone playing Angry Birds, and she say she "doesn't like it" can I get mad?
I'd say you can't judge anything too well if you're not giving it enough attention, but it depends on the piece of work. But then these kind of judgements are largely subjective, so if somebody can't get through a particle experience with some added distraction then it tells you as much about their tastes as the value of the content. Also, demanding attention may not be a good thing. Yahtzee turned distractions off for Far Cry Primal because audio awareness is an important game mechanic. It's not critical to The Division, or Rocket League. It doesn't mean Far Cry Primal is a more engaging or enjoyable game than Rocket League.
I'd say the biggest change I've seen in games, particulary reviews of games, is the shift away from worrying about production, i.e. basic mechanics, graphics, it's basic functionality and playability, and a massive focus on "the experience". This is because games can pretty much be anything they want now. We're not as restricted by processing speed, fidelity of image, possible game mechanics, etc. Now we focus on the art. How does it feel to play it, is it frustrating, thrilling, too tense, dull. Does it look beautiful, regardless of whether it's 8-bit or 1080p, but more importantly did the developers choices enhance or diminish the gaming experience?
I feel anyone else's subjective opinion, useful or not, should never be given more value than your own. Good example, while with a group of friends I mentioned Starship Troopers and what a great film it was. Another friend nearby overheard and said "No!! It's a terrible film!!? All macho bullshit and guns, bleurgh!" We debated back and forth for about 15 minutes over the fact that it's a parody of that kind of thing and I felt she'd missed the point. At this point she says "Well, I did stop watching after the first 15 minutes"..... So when hearing anyone's subjective opinion, keep in mind they may not experience things the way you have.