The "guides" are generally wrong on the details... Schanuzers of all sizes (and the related Pinscher breeds) are German working breeds capable of a variety of tasks. Generally, the largest was used for guardian tasks, military, and occasionally drafting or herding: the short haired Doberman Pinscher was primarily on the guardian side, the wirehaired Giant Schnauzer did more of a variety. The smallest was used for vermin control and a little bit of general farm work (i.e. livestock guarding, a tiny bit of herding or small game hunting) and eventually evolved in more of house pets, this is the Miniature Schnauzer and the Miniature Pinscher. The middle sizes dogs did a little bit of everything, this is the Standard Schnauzer and German Pinscher.
A Miniature Schnauzer is basically a terrier, so they would be good at vermin control in barns & buildings and would perhaps be able to hunt small game like rabbits or squirrels. They don't have great pointing or retrieving instincts, but with dedication and training could be decent at flushing game birds and possibly retrieving them as well. For serious hunting, you need to get a kind of dog bred specifically for the game species and style of hunting that you want. Dogs in the hound group will chase based on scent or sight, dogs in the sporting group are primarily for hunting birds. Terriers (like the Mini Schnauzer) are good for vermin control and for flushing game that has gone to ground.
Miniature Schnauzers are capable of quite a bit... actually, like most terrier breeds they tend to think they are capable of more than they are... and start fights with other dogs or game animals too large for them to actually take down. If you are looking for fun dog sports in general, I have seen Mini Schnauzers compete quite successfully in rally, obedience, agility, and tracking and (depending on the individual dog) sports like freestyle, dock diving, flyball, and even lure coursing can be fun as well.