Overall, the game is more reactive to the show than vice-versa, since the lead time on TV is such that the season has to pretty much be complete (or close to it) before the first episode airs. Though there's the possibility that something in the game might affect the second season.
The game on the other hand, gets updated with a bit of new content every week based on the episode that aired that Monday. This content so far comes in three forms. Episode missions are missions added to the game that involve your character fighting/exploring alongside characters from the show (that you have to complete that week or they disappear, since the event is over by that point). Pursuits are achievement-like tasks that involve finding audiologs, fighting enemies, and participating in PvP. Contracts are like bounties for different factions that change daily/weekly. Every week you get a new mix of these things, in addition to the game's story/side content that's always available.