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You wrote, "Despite it acting like a dimension in my view." I think what you're imagining is that because the TableMinGrp is making visual partitions in the view that it's a dimension, when in fact it's a discrete measure and it's the "discrete" part that is visually partitioning the view. There are two distinctions we need to make, dimension vs. measure and discrete (blue pill) vs. continuous (green pill). See http://www.theinformationlab.co.uk/2011/09/23/blue-things-and-green-things/ for more information.
Tableau can partition table calculations by dimensions, and partition table calculations by discrete regular aggregate measures (by turning off the "Ignore in Table Calculations" flag for a discrete measure), but it currently cannot partition table calcs by other table calcs except through some rather complicated workarounds.
The TableMinGrp is a nested table calculation that is doing a variation of the Find First/Last/Min/Max problem that I wrote up inhttp://community.tableau.com/thread/137236. My suggestion would be to use one of those techniques to pre-calculate the TableMinGrp so it can be a dimension, potentially an aggregate measure.
I know this is 5 months late, but couldn't you get the cumulative play you are looking for by using the PlayerDay table instead of PlayerSession? I am assuming you are working with IGT, correct? I haven't done this level of detail on table games as they are not large portion of my casino. I am thinking you can get what you want by working with Table_Sessions, Table_Games & Table_CashBuyIn within the PlayerDay table. I know the PlayerSession can give you more info than you want in some circumstances.