Honestly, I would just calculate a focal variance. Variance within a 3x3 window is very close to TRI
[sqrt(sum(dev^2)]. The variance would also be more scalable than TRI which is limited to a square 3x3 window. You could use the raster calculator to calculate an algebraic approximation of the index.
ArcGIS (type) syntax:
s = FocalStatistics(dem, NbrRectangle(3, 3, MAP), "SUM", "")
d = (dem * dem)
t = FocalStatistics(d, NbrRectangle(3, 3, MAP), "SUM", "")
tri = sqrt( t + 9 * d - 2 * dem * s )
There are several geomorphometric indices available in the ArcGIS Geomorphometry & Gradient Metrics toolbox that would provide alternatives to TRI. There is an actual implementation of TRI, that provides optional corrections and standardization of the index, in the R spatialEco package available on CRAN or GitHub.