Maybe I didn't explain right:
Imagine he has only one game, and that he last moved on 6-Jan. If that is a 5-days-per-move game then he would timeout on 13-Jan (because of weekend). Now, he times out on 13-Jan the first time, so that will be his first vacation day. He is given an extra day, so he timed out again on 14-Jan, being his second vacation day. and so on (excluding weekends) till he times out for the 31st time, on 24-Feb, this time for good.
So, to know exactly when his vacation days are over, you need to find out the fastest game he has and start calculating the number of vacationed days from there...

Of course, it's easier to just wait another week