Dear Georgina,
You probably well describe how many feel when they read this - even me had I not written it! Yet unsettling as it is, the question deserves consideration because people are asking it.
Re what is reality, your example is telling. A computer game can be "real" to one so involved in it they see nothing else. It is a local reality, a world real within itself, even though from outside, it is not real. So what is real can arise from the unreal, e.g. in a Japan, an assault court case arose because in an online game, a player lent his special sword to another avatar in the game, who then sold it on e-bay! So was the sword that was stolen real? Or take the classic case of Mr. Bungle (actually a group of NYU undergraduates) in LamdaMOO, a text based virtual reality, who hacked a voodoo power, to control other players, and used it to violently "rape" several female characters, making them respond as if they enjoyed it (Dibbell, 1993). There was no "real" rape, as there was no physical contact, and no laws were broken, but there was outrage. Or if a wife's husband commits virtual adultery in a game room, should she leave him? Was it real?
Lets define reality as whatever is the "end of the causal line", i.e. uncaused. In The Matrix, the construct world was created by machines in another world, where Neo is a body in a vat, so is unreal. In contrast, the physical world of Zion is real because it is not caused by anything else. The VR conjecture is NOT The Matrix because it asks if that physical world is self-sufficient, given the big bang, quantum randomness etc. Whether the physical world is an objective reality, that exists entirely in and of itself, is a question science can address, because it is about the physical world.
You ask if virtual reality is compatible with science? Suppose one day the processing behind the virtual online world The Sims allowed some Sims avatars to "think". To practice science, they would only need information to test theories against, which the virtual reality could provide. If they found a world like ours, e.g. with malleable space and time, they could conclude their world was virtual from how it behaved. So not only does science allow the virtual reality conjecture, but a virtual reality could also allow science.
Finally, to conjecture the world is virtual (p1) then say it is digital (p9) would sidestep the contest question, but in between are seven pages on why this is possible and how it could be so. What then about the many other things not covered? Well it is currently just about the physics, not psychological or philosophical implications. If you are wondering if it supports new age ideas of telepathy, psychokinesis, aliens, crop circles, etc, I dont think so, as why should a simulation let its avatars change their programs? Yet equally, it does not deny that possibility. It is just Tegmark's "physics from scratch" approach where processing is the only initial assumption.
all the best and thanks for your comment
Brian Whitworth