Instead of having the dimension on the Filters Shelf, put it on the Pages Shelf. However the play button for the Pages Shelf only works inside Tableau Desktop or Tableau Public, it doesn't work for web browsers.
Putting the year filter on the Pages Card solved a problem for me I have my year values on a slider in the Filters Card. Also on the slider is an "All" value. I'm working with time series data and an "All" was summing up my label field across all years. It makes absolutely no sense to sum my data across time. When I moved the Year to the Pages Card, only the year values are showing, "All" is gone!
Another benefit of using the Pages Card is that there is now an "animation" feature along with the slider feature.
I'm using 7.0.