RMS can be determined as .707 of peak, and peak can be considered 1.414 times RMS values for a pure sine wave. Peak to peak is double the peak value. So using the numbers you quote I suspect the unit does not generate a pure sine at the output but instead generates a somewhat “spikey” AC output, which probably changes a lot once the arc is struck.
Anyway, if you go by the numbers, the 10kV rating is probably an RMS one. Arc striking capability is probably determined mainly by the peak voltage since it is exactly that, the highest instantanious, absolute potential generated, which might make reference to RMS numbers with an electronic unit somewhat of an understating far as gap settings are concerned. Undoubtedly you can dig up some more information on the relative use of the part you gave. Without knowing any better, I might use it in equipment designed and adjusted for a 10kV reactive ignition, and if I get misfires I’d reduce gap until I didn’t get misfires. Hopefully you can come up with something better than that. :)
For a sine wave output, peak-to-peak would be the RMS (square root of the sum of the squares) voltage times the square root of two. From those specs the output is probably not a sine wave though. With a regular transformer the output would probably be closer to a sine wave so the 10kV would be the RMS figure.