"What, you've never seen a woman hanging out and enjoying herself before? Fuck off!" was the vibe I got from the ghost. She was definitely more pissed off about the guy peeking than the guys being there in the first place. This lends credence to the guy rationalizing that one of the conditions for the ritual to work is that there has to be living people in the house. Perhaps if the house is totally empty she will try harder to leave and seek the house owners?
IMO the ghost was the son's lover. It is likely she committed suicide (or perhaps the family even killed her) in that room and her grudge allowed her to haunt the family, possibly with her powers getting the strongest around the time of her death's anniversary each year, hence the house-sitters only getting hired for summer. The ritual is seemingly designed to keep her confined to the spot where she hung herself whenever she manifests, and it does work to an extent. But, it is obvious that she is still getting stronger anyway, since she was able to leave the ritual room and troll the two sitter dudes, if only weakly. And now that the dudes totally failed the ritual, she has become strong enough to manifest during daylight hours and even leave the room. RIP houseowners.
The son probably didn't know about the ritual which is why he was pissed off by the house sitters calling his parents at night, and his parents told him the truth afterwards which caused him to make that apologetic second phone call.
The shooting game prizes might have been memorabilia collected by the woman or the son which serve as a reminder of her earthly life and were used to bind her to the room, and perhaps the prizes have to remain standing upright so she will be too busy knocking them all down to leave the room. Another condition of the ritual is that no one is allowed to see it - which might explain why she immediately was able to leave her spot to scold the guy peeking through the window.