R-EXT connection on the STP16CP05MTR LED sink driver
The R-EXT resistor in figures 17-18 of the datasheet is shown connected to the R-EXT pin at one end, and a not-very-commonly-used symbol for Ground, at the other end. Thus, the resistor does need to be connected to ground. 

Notice also that the GND pin connects to the same symbol, such as in Figure 17.