OK, this is genuinely hard. I gave up and rang TFL, and was on the phone to them for half an hour, during which time I was assured that "non-Gatwick-Express services GTW-VIC don't count towards the cap". I drew their attention to this page, which says
Journeys on Gatwick Express do not count towards caps, but those on Thameslink and Southern services do count towards caps.
at which point they agreed that it was a difficult problem. Finally, after firing up the Big Difficult Question Computer, they assure me that (at the time of writing), the Oystercard single adult fare from GTW to VIC (not via Gatwick Express) is £16.20/£10.20 on/off-peak, that it will count towards a cap, and that the cap is £30.50/£19.00 on/off-peak (this is a National Rail cap figure, specific to journeys between GTW and zones 1-9). That means you'd pay for your next £14.30/£8.80 of TFL journeys in zones 1-9 (sic), after which time everything else eligible inside zones 1-9 would be capped.
I had previously written, and other local authorities agree, that you can both make the journey cheaper, and lower the cap, by getting off at East Croydon and tapping out and back into the station. This will lengthen your journey by at least 20 minutes, but saves money. Note that I have not confirmed this theory with TFL (it seemed likely to provoke a breakdown in the very nice customer service lady who had thus far been very helpful). Check the edit history on this page if you want to know more about that.