Well... actually... having a laptop with you is basically for the 2 hours you will be waiting before boarding the plane. One on the plane... go to sleep (if you can) because there is no room for anything. You can work on your laptop until you get a Coke served. I mean... the experience is embarrassing.
If I arrive at the gate more than 5 minutes before the plane boards then I am way to early. No need to be there two hours early.