DS1100L Why Would You Want a Delayed Signal?
Clearly, they wanted to get a more accurate estimate of the phase of the input signal transitions relative to the CPU clock, which is presumably on the order of 33-40 MHz (\$\frac{1}{30 \text{ns}}\$ to \$\frac{1}{25 \text{ns}}\$).

GPIO inputs are fed through FFs inside the microcontroller in order to avoid problems with asynchronous sampling and possible metastability. This limits your ability to measure the phase of a transition to the clock period (25 ns). By providing multiple delayed copies of the signal in this manner, you can determine the phase with a resolution of 5 ns by looking at the pattern of bits captured in the FFs.

                        _________________|__________________________
signal  _______________/                 |
                             ____________|__________________________
signal + 5ns  ______________/            |
                                  _______|__________________________
signal + 10ns ___________________/       |
                                       __|__________________________
signal + 15ns ________________________/  |
                                         |  ________________________
signal + 20ns ___________________________|_/
                                         |       _____________________
signal + 25ns ___________________________|______/
                                         |
                                         +---&gt; 111100


For example, if the CPU clock should happen to fall where I've drawn the vertical line, you'll read a pattern of "111100", which tells you that the signal transition occurred between 15 and 20 ns before the clock edge. This gives you the same timing resolution that you'd get with a 200 MHz sample clock, but without requiring a processor that can run that fast.

BTW, the generic term for this kind of encoding is "thermometer code".

If the goal of the system is to measure the frequency or period of the input signal, this approach allows you to achieve a given level of precision in 1/5 the integration time, which could be significant in a production environment.