That table is showing the various voltages created by using a voltage divider circuit on the output of the Wind Vane using a 5V supply and a 10k resistor. The voltage will vary and can be read by an analog to digital converter. Any of our Weather Shields like the [SparkFun Weather Shield for Arduino will have that voltage divider circuit built-in and the output is sent to an available analog pin to read that voltage and return a direction.
Per the document, the magnet in the vane can activate two adjacent reed switches at once when half-way between the 45 degree points. The values for the 45 degree points are for a single resistor (33k, 8k2, 1k, 2k2, 3k9, 26k, 120k, 64k9). The values for the points between these are for two resistors in parallel (ie. 22.5 degrees is 33k || 8k2 which works out to (33 * 8.2)/(33 + 8.2) = 6k57. The values for the 45 degree points were chosen to make the 22.5 degree points work out to values that are suitably different from each other and the 45 degree resistors to allow for reliable measurement given part tolerances)
From a software point of view, just create a table and test for a match with some tolerance.