There's nothing odd about it. Because if he was there, he would be the odd one out. Four girls who all love Kirito. I reckon Klein knew from experience the girls would start to chat about Kirito with lovey dovey eyes, so he would feel himself if not plain unwelcome, at least an extra in that company. It's a different matter when they are actually playing the game by going through quests. But now there was nothing of that sort.
It was all meaningless. They can't force Asuna to marry some douche when she already has Kirito. Even if they don't respect her wishes and the fact Kirito saved her life twice (and ten thousand other people. After all, it only matters who's Kirito's father is and isn't), it's still meaningless. Kirito is already apparently raking in money, and that will only accelerate later. Maybe he can't provide Asuna with a fancy mansion in RL right away, but looking at those two, it doesn't matter. If her family would try to force her into something, she would just leave the family. She gained full mental indepence already during the SAO when she had nobody but herself to rely on. She will only humour her family to a certain point.