Sorry

Unfortunately, streaming is a very data intensive activity, especially if done in hi def.  According to Netflix, the amount of data needed for streaming is 3GB per hour in HD, 700MB per hour in SD, and 350MB per hour in LD.  

Regarding online gaming, though some online games do work just fine with satellite internet, real time games, like first person shooters and other types of action games, don't tend to work well because of the high latency inherent to satellite internet.  Those latter types of games may work, but they'll most likely be very frustrating, at best, as what your son will be seeing on the screen will actually have happened at least a half second before he sees it.  With online action games a half second can mean everything.  The delay is just too high for most of those types of games for them to be even playable.  

Games also use a lot of data, especially if it's done with a console and there are game updates.  Some of those updates can be very large.  

My advice would be this:  If you feel that the representative during your sales call misled you as to what you'd be able to do, I would request a sales call review.  If it's determined in that review that appropriate expectations were not set by the sales rep, you may have recourse regarding the Early Termination Fee if you choose to cancel the service.  

With what you say you have used, data wise, in just a day or two, there is no way that the data will last an entire month, even if you had the largest plan (50GB), and you're likely to exhaust your monthly data allotment and have your service speed throttled in a relatively short amount of time.  You can try to adjust your usage habits and your son's game playing habits to make the service work for you, but I don't know if it really will, unfortunately.  :(  

You can request the sales call review in this thread.  When you do a rep will put in for the review.  It can take a day or so for a rep to reply, and it usually takes at least a day or two for the review (sometimes a bit longer), and with it being so close to the weekend it's likely that you wouldn't hear the results until next week.