Moore's Law was an observation made over 40 years ago that to some extant is still seen today, it is not an actual law by which companies oblige to. In reality the trend is slightly different, it demands mostly on economics and marketing. Intel will continue to provide the best possible chips regardless of Moore's Law.
It's mostly driven by competition. I think if AMD were gone, then Intel would still invest money in research, however, the goal might not explicitly be to make the chips faster. Moore's Law is really just a side effect of the process technology. Currently, the transistor size gets cut in half roughly every two years. Back in the 90s, it used to be every 3, but because of competition or other factors which I am unaware, they now shrink it about every 2. Which is pretty amazing considering that going from 90 to 45 nm is a lot harder than going from 2 um to 1 um...well, maybe not because more technology is available when shrinking from 90 to 45 nm. Anyway, the smaller transistors have 2 effects with regards to performance. One is that the physics of the transistor improve and the other is that since the transistors are smaller, more can be crammed in the same area as before. The architecture designers also perform some optimization and tricks to get more performance out of transistors, but only so much can be done here and it's really the process technology which most influences the power and cost of the processor (and the profit of its manufacturer). The reason I think Intel would still invest in R and D even without competition is because it still benefits them to make smaller transistors and improve yield. Ignoring competition, they would want to produce as many functional die per wafer as possible. So they would still try to shrink the transistor and improve yield, but this might happen at a slower rate if there were no competition.