Perhaps you could email the company and ask how long the activity is. I imagine they have a safety briefing and you'll need time to gear up and take gear off. Then there is the time to get to the airport - could take 45 minutes.
I wouldn't chance it, especially if it's an international flight!
I agree about the timing being too tight for comfort. If you are going to the airport on a weekday, allow a good hour to go from Skytower to airport. Commuter rush-hour in Auckland is a slow process.
Consider forgoing the skywalk and just visit the observation decks for 30 - 40 minutes to fill in time. If you have a rental car, perhaps visit Cornwall Park and One Tree Hill instead of going into the CBD.
If you're leaving Rotorua at 12, the plane gets in about 1235 from memory, and given it isn't rush hour, you should comfortably be able to get to the sky tower by 2pm. So is an earlier booking there an option? I agree with others that leaving sky tower at 5ish for an 8pm flight might raise your stress levels more than you really need...
Thank you everyone for your replies, I just emailed the company and already have my question answered.