Why aren't there any competing biologies on Earth?
There are indeed almost certainly other potential alternatives to DNA-based biology and the RNA-based biology that may have predated it, which could be used to form viable organisms.
Many of them likely have some energetic disadvantage relative to DNA and RNA (e.g., requiring a higher bond formation energy, having a less flexible backbone) and those would naturally be expected to be outcompeted. But some probably aren't so different from DNA and could indeed have formed a viable alternative---if nothing else, the opposite chirality molecules are certainly candidates. Why aren't alternatives still around?
Surprisingly, it turns out that when time scales are long enough, we should expect a natural loss in the number of different independent lineages. Another more recent example of this is the fact that all modern humans are descended from Mitochondrial Eve and Y-chromosome Adam, despite the fact that these two individuals were members of thriving human populations at entirely unrelated times. Biodiversity is constantly being gained through divergence of existing lines and lost through lines that fail to reproduce. Over many generations of reproduction, this produces a random walk pattern that converges toward elimination of all but a single lineage in a given population even if all lineages are equally fit.
Now back to the origin of DNA-based life.  If abiogenesis is a rare and difficult event, then we would expect only one or a small number of life models to have emerged billions of years ago. Random fluctuations over all that time will tend to drive all but one toward extinction. With evolution at play as well, any lineage that randomly gains an advantage will be even more likely to outcompete the others.
And once there is life of any sort around? Well, potential alternatives to DNA are still nutrients, and therefore will simply be eaten by existing life forms before they have the chance to evolve into something new and interesting.