When I bind a templated column to a datetime and set allowfilterrow to top and filteringscope to columnlayout then the filter does not work for this column:
When the datetime of a row equals the datetime entered in the filterrow => no rows are shown.
When I click the removefilter icon, the removefilter icon stays visible.
See also attached files.
Looking over your sample:
In your data creation you are using DateTime.Now. A DateTime object will contain a Milliseconds property which is not shown in the normal ToString() representation of the data. So if you type into the filter box the exact thing you see into the cell, the Millisecond value will be different (it will default to zero, but he value from the DateTime.Now will more then likely not be zero) and the filter will fail.
If the Time aspect of your filtering is not important, then you could use the Date Column rather then a Template Column.
The RemoveFilter icon issue was replicated and will be resolved in a future service release.