Well, no, the GOP didn't "own the world," we just thought we did. Newt sold a great political gimmick, the Contract for America, and a voting public that was sick of Bill Clinton's crap went for it.
Unfortunately, selling the Contract was not the same as implementing it. Newt was not the man to implement it; and it turned out that support for the Contract was not all that deep after all; and the GOP had no way to counteract the media blizzard. Bill Clinton revived his presidency on the basis of Newt Gingrich's Speakership, and the Contract was not particularly effective in any case.
Since then, the GOP has gradually lost whatever direction it had as various single-issue factions began to tear each other apart, and narcissism and opportunism has supplanted principles.
I think Newt deserves a little more credit than you give him for the Contract with America, after all it brought House Republicans in from the desert after 36 years, no small feat. Without the Contract's success in '94, America would never have seen welfare reform or a balanced budget.
And, Gingrich also deserves some credit for reducing government spending. Sure, spending still rose, but as a percentage of GDP it shrank for the first time in decades. Certainly, a lot of that is because of the fantastic economic growth in the last half of the decade, but I believe the country's robust economic growth was because of policies that Newt helped to shepherd through Congress and make Clinton sign kicking and screaming.
The GOP didn't do itself any favors by impeaching Clinton. It may or may not have been the right thing to do morally or legally, but it turned out to be a disaster politically. I actually think the GOP really started to decline after Gingrich left and when Delay took over in the House. Delay was a tremendous whip, but a horrible leader - the peter principle on full display.
Lastly, I think the media really sharpened their knives with Gingrich and it was an object lesson on how powerful the traditional media really is. Clinton used, abused and destroyed Newt with the help of a very willing accomplices in the media.