Given that all the "best" discussions are about opinions there are of course no rights or wrongs, but the motivations are often interesting. If you aren't particularly fond of a player you can go to some lengths with your arguments.
The Association of Chess Professional's president Sutovsky doesn't rank Nakamura as one of the ten best players of 2015. The given reason is that he didn't win any strong classical only tournaments. In this he forgets FIDE Grand Prix in Khanty, and while Zurich was half rapid Nakamura did well also in the classical half. He also won strong opens ahead of players like Caruana and Topalov, and the US Championships ahead of So.
Svidler had a bad year without winning anything, but is still 7th on Sutovsky's list. Karjakin is even ranked 2nd thanks to winning the World Cup. There Sutovsky has no problem with Karjakin's neither winning final, semi final, quarter final or the round before that in classical chess. All these minimatches (and more) were won in rapid/blitz.
My best chess player in the world list for 2015:
1. Carlsen - no motivation needed apart from looking at the results of Gashimov Memorial, Wijk aan Zee, Baden-Baden, London, Qatar and World Rapid Championship.
2. Nakamura - Especially Zurich was a good win, but also Khanty, Gibraltar, US Championships and Millionaire Chess makes it easy to place him second on a list like this.
3. Giri - didn't win anything else than the Dutch Championship, but his repeated top results, especially going an undefeated +5 in the Grand Chess Tour, make him top three on my list.
4. Aronian won Sinquefield Cup a full point ahead of Carlsen and seems well on the way to his best form again. Maybe should be a bit further down going by some bad results, but the very impressive Sinquefield performance is enough for me to place him 4th.
5. Anand. Best score in Zurich classical half, and good results as 2nd in Gashimov Memorial and Norway. Also some weaker results, but the first half of the year makes him an obvious top 5 candidate here.
6. MVL won Biel and came an inch from winning the whole Grand Chess Tour. He should be placed quite high here after being 0.5 from first in Wijk aan Zee and reaching that tiebreak in London.
7. Topalov won Norway and reached his highest rating ever. The rest of the year was so-so, but few players have won as strong tournaments as Norway.
8. Kramnik gained rating and won some nice games in team events. Especially the European Club Cup was great. Otherwise a year to forget for Kramnik.
9. Karjakin won the World Cup and played well on occasion, especially in the Russia-China match.
10. Wei Yi had some great games and passed 2700. Together with his winning the Chinese Championships and Wijk aan Zee B he could be included here for his age.