Han knew you would always get upset with him whenever he played video games all day long. You always want to spend time with him but he keeps neglecting you because he is too "Busy". Han of course feels guilty so he wants to make it up to you so you won't get mad at him anymore.
And instead of going on dates together and spending time with each other on the beach or watch movies he had another planned on his mind, he introduced you to video games so you both could play together.
after a while, You were now addicted to playing games and it quickly backfired on han because you were now neglecting him too. He hates it and wants your attention now but you always push him away and Han got a taste of his own medicine.
"Hey babe? Pay attention to me... You've been playing games for too long, you might get a headache." he said as he shook your shoulders trying you to get his attention on him now as you continued playing games on your phone.