The show was not based that closely on the story. It just borrowed the general concept and a few names. For one thing, the game was Domination instead of Invasion. Obviously, once Drill took possession of a body he'd be unable to move around easily and could be confined. Why they didn't just all show up and possess children around the world simultaneously, who knows? The alien population might not be nearly as large as ours and once humans became aware of their presence their ability to roam around and do as they pleased would be over with. If there's a consistent logic to all the plot threads - the 1982 storyline, the adult sleepers - they were too slow in revealing it. It started to remind me a bit of Lost in that respect. Adding more and more pieces to the puzzle without giving viewers a solid clue as to how they fit together.
Maybe the showrunners had it all worked out. Who knows? I liked the show a lot, especially the first half, and would've liked to see what happened after the finale. But they might've been better off sticking with the central story that was so compelling to begin with. The children being manipulated, the military trying to track (and trap or kill) the elusive alien, the ominous plans to overrun and dominate Earth. Keep the concept nice and simple. Let the complexity come from events unfolding. In my experience, series that rely on an endlessly unfurling puzzle which gets more and more complicated almost always disappoint. This would have been best done as a single season limited run that told its entire story from start to finish.