No, that computer is good enough. It's the devs making the app you played that are not.
Oculus is playing a game with their specs. On one hand, it makes their peripheral look like really cutting edge technology if it can only run on the latest and greatest hardware. And on the other, it keeps them from having to try to fulfill even more orders over what they have already proven they cannot handle.
Simple graphics + room scale VR is an amazing experience. AAA games need whizbang graphics features to be able to compete with each other because they haven't had any new gameplay features to show off in nearly 15 years. But a lot of this effects are unnecessary in VR--sometimes even a bad idea! Normal mapping, for example, is has been reliably shown to cause motion sickness in people with a relatively high ratio of estrogen to testosterone (not just women, but men with hormonal imbalances. Women with high testosterone seem to do fine).
I think Valve and Oculus understand that AAA game studios don't have a lot to offer to VR. You're not going to really adapt Call of Duty to the Vive. So they are banking on the huge cadre of indie developers to rapidly make the first content for them. And that is going to mostly be fairly new devs using Unity, not really understanding what they are doing other than following tutorials. Optimisation is not exactly a strong point.
This study went into some of the changes in depth perception experienced by people going through hormonal therapy for gender reassignment operations: http://www.ncbi.nlm.nih.gov/pubmed/10341369
Good enough for what? I used the first build of WebVR with my DK2 on 2013 Macbook Pro and tried a simple Quake level viewer. Sure, no AAA graphics but it worked, and well!
The new drivers removed my ability to experiment with WebVR. I could no longer use the hardware not due to limitations with my computer, but limitations imposed for marketing purposes.
