Are chess players getting better over time?

Mostly.  Kenneth W. Regan and Guy McC. Haworth analyze games move-for-move, using chess-playing computer programs.  The result:

…we conclude that there has been little or no ‘inflation’ in ratings over time—if anything there has been deflation. This runs counter to conventional wisdom, but is predicted by population models on which rating systems have been based…The results also support a no answer to question 2. In the 1970’s there were only two players with ratings over 2700, namely Bobby Fischer and Anatoly Karpov, and there were years as late as 1981 when no one had a rating over 2700 (see [Wee00]). In the past decade there have usually been thirty or more players with such ratings. Thus lack of inflation implies that those players are better than all but Fischer and Karpov were.