The filter shown just works for the map and I don't know how to expand its functionality to the web. In the tutorial video about "Dashboard Development" they do it via the menu entry "Apply to worksheets". But I don't have this entry ... In another tutorial they do it via "Make global" - but this entry is missing as well.
The reason that the quick filter is not working is because it is being used with Measure Names. The best way around this would be to reshape your data so that the years are all in the same dimension. The following KB articles will give more instruction on how to do this: