Badly worded article, the general consensus is you will have an activation code in the box like you do a PC game that will tie the game to your gamertag so youd have to be online for the security check to happen.
"Microsoft’s next console will require an Internet connection in order to function, ruling out a second-hand game market for the platform."
That statement doesn't completely make sense to me. Just because you have to have an internet connection doesn't necessarily have to mean there will be no second-hand market...those are two complete separate things. Maybe there will in fact be no second-hand game market but it won't ONLY be because your XBOX must be connected.