You can't truly judge any player's Olympic campaign until it's over, but we can tell you how all six Kings are faring in Sochi. Of course, all six have made the quarterfinals, so team performance is only a small factor here.
1. Anze Kopitar, Slovenia
The surprise factor of his team's run puts Kopitar on top, though it's really comparing apples and oranges to the other Kings Olympians, isn't it? While other Kings are contributing for gold medal contenders, Kopitar is the one and only for his team, and he hasn't shied away from the spotlight. Kopitar has two goals, one in each of Slovenia's two victories, and has helped carry his team to a surprising berth in the Olympic quarterfinals. For better or worse, he's only ninth on the team in shots/60 minutes, so he's certainly getting others involved.
Kopitar's doing it all. Aside from the scoring, he also hasn't been on the ice for a single goal against at even strength. His line generally controls possession, which I'm sure is no shock to those who watch him regularly. And despite missing almost half a game due to a stomach ailment, Kopitar still has the eleventh-highest average ice time among forwards at the Olympics. Without that hiccup he'd be #1 or #2 behind Mats Zuccarello, the other sole NHLer on a team. Zuccarello's Norway team finished in last; Slovenia's playing for a spot in the semifinals.
2. Drew Doughty, Canada
He's doing it for a much better team than Anze Kopitar, of course, but Doughty has been downright prolific in three games at the Olympics. He leads all defensemen with four goals and is tied for the points lead with Erik Karlsson, who you might know as the leading scorer among all defensemen in the NHL right now. (Doughty is tied for 20th.) The work on the defensive end has been just fine, so the story has been the offensive fireworks, especially since they haven't been on high-percentage shots. That doesn't bode well for his chance to continuing scoring those type of goals, but it's been a nice surprise on top of his consistent play at the back.
3. Jonathan Quick, USA
Dan Bylsma and the Americans have been naming their starting goaltender on a game-by-game basis, and for tomorrow's game against the Czech Republic, it will be Jonathan Quick. That's no surprise, as Quick got two of the three starts in the opening round and excelled. His lone goal against in the first game shouldn't have counted, though the hockey gods compensated by disallowing a potential go-ahead goal against Russia. Quick came through when it counted in that one, stopping Kovalchuk and Datsyuk juuust enough to give America the win. He's set himself up to get every start the rest of the way, so look for him to get the lion's share of credit or blame depending on how the team does.
4. Jeff Carter, Canada
He's got a hat trick in the tournament, and he's fourth of six? Underlines how well the Kings have done in Sochi. Carter, for his part, has played his part well for the Canadians. They've asked him to shoot, and he's leading the team (easily) in shots on goal. He picked up a natural hat trick against Austria, from a combined distance of five feet or so... so he's going to the right spots! And his ice time has ticked up, as he's now right around the middle of the pack on the team. As one of the most-criticized picks of the Canadian management, he's done pretty well.
5. Dustin Brown, USA
Par for the course to this point. Make a controversial hit. Score a goal. Be annoying (and now, be annoying on a line with other annoying people!) He also contributed to one of the great GIF moments of the tournament, which means nothing but is still nice. Brown has been relatively lightly used by Team USA, as he and T.J. Oshie have the lowest ice time among forwards who have been on a regular line in all three games. (Blake Wheeler is the unusual 13th forward.) He does have the aforementioned goal, though, and he hasn't been on the ice for a goal against all tournament. He hasn't dazzled and probably won't, but he'll get a regular shift for the rest of the USA's run.
6. Slava Voynov, Russia
A quiet Olympics so far for Voynov. As expected, he's gotten significant time for the Russians, and with the team moving to the quarterfinals with only a shootout loss to the USA, they're doing just fine overall. Having said that, it's not good when the only big story revolving around a player is negative. Voynov drew headlines for hinting that Quick had knocked off the net off its moorings on purpose late in their showdown, which prevented a go-ahead goal for Russia. Voynov is without a point so far but also has not been on the ice for a goal against at even strength, so he's been... neutral! Going forward he'll play an important role for Russia, who likely needs to beat Finland and Sweden just to make the gold medal game.