Buyer beware. You need to know what you are buying or in this case what you are sending as a gift. It is a pretty simple concept. You buy or receive the drink, and it lasts as long at the description states, regardless if you are playing or not.
It is clearly stated in the product description how the Boost works(read the bold)
Earn experience points (XP) faster so you can level-up more quickly and unlock new equipment upgrades. Provides a 5% increase. Available in 1 hour, 2 hour, 4 hour, 12 hour, 1 day, 3 day, 7 day, and 15 day durations. Takes effect immediately upon purchase and are based on real-time.
One week of boost if lasted only during game play could last some players years. Now does that make sense?
Cheers,
b0gey