Anzhi at that time had a project going by local billionaire Suleyman Kerimov to become one of the top Russian teams. Hiddink as manager and Eto'o were the key parts, but they also bought a lot of other solid players at the time before Kerimov pulled most of his financial backing a few years later and they went back to being a yo-yo club.
Eto'o obviously only went there for the huge salary, but watching his games there you could see he was beginning a decline despite working his arse off and being very professional. The level he was playing at would have seen him be increasingly peripheral at a top Italian club/other top 4 league club. He would be quickly moving to a mid-table\Europa league sort of side if he wanted to remain a consistent starter among the top-tier of leagues.
The guy probably knew he was struggling to keep up the week by week intensity needed, so he goes for the money by taking the step down to a lower-half of the top ten ranked Euro league side where he can still play at a decent level and be a starter. It's not like he instantly went to the middle east or somewhere similar. i'm not sure where the RPl was ranked that season, but i'm guessing it was around 6-7 in the Euro coefficients. It's not a level you can just arse around and play like you're half-retired and are likely to get away with it for long.
Watching Eto'o for Anzhi, he was still good and played a big part in carrying them to their best ever league positions and a couple of decent europa league campaigns, but you could see he was no longer as mobile, quick or sharp in front of goal as before and in his first season you had other forwards like Seydou Doumbia and a similarly aging Aleksandr Kerzhakov scoring quite a bit more goals and matching\exceeding his level of play, plus guys like Kevin Kuranyi, big Dzyuba, aging midfield playmaker Igor Semshov and former liverpool flop Andrey Voronin scoring a similar amount.
Second season he was very good in Europa league, scoring 9, but only scored 10 league goals, less than ahmed Musa or Yura Movsisyan and though his overall level of play was still superior to players like that, it was pretty obvious he had become just another solid\good but far from great player at this stage in his career. which was more or less confirmed when he then tried to get back playing in higher rated leagues with Chelsea, Everton and Sampdoria. If anything his peformances in Turkey and getting that amount of goals again for a couple of seasons without playing for one of their best clubs was a good later career revival.
in feckin Florida. Not to mention the alcoholism and philandering. (