If I remember correctly, in Hearthstone if you haven't played card in time you have once - you'll get "roped", nothing is played. If you still haven't played anything in next turn, "rope" starts earlier in order to reduce waiting time for other player.
In Gwent, I guess the system could be the same - if your opponent haven't played anything, his time to make a play reduces ("roping"). If you passed your turn and opponent still haven't played anything - you get a win for current round
Well having the enemy pass would be the easiest solution. This game does not take as long as a hearthstone, and you have only 1 play to make each round, so timing out should be less of an issue.
Playing random cards, can also mean you can just go afk and let the game play for you, which is something I do not want to have, especially since the enemy always has to wait the maximal time per round (which of course could go faster the second round like in hearthstone, but still it would be annoying).