To test whether the preceding algorithm (or for that matter any card shuffling algorithm) is truly random you should perform a few tests:
  1. Over a number of shufflings (100,000 lets say) what is the percentage of a particular card appearing first?
  2. From the same pool, what is the percentage of a particular suit appearing first?
  3. What is the percentage of particular rank appearing first?

If over significantly large number of games the results approach the mathetmatically predicted ones (that is 1/52 is a chance of first draw being ace of diamonds, etc) then we can safely conclude that it's really random.

Note that the algorithm should also work for multiple card deck games.