Because those nucleotides occur naturally.
...probably. We've been finding the building blocks of DNA on meteorites for a while now. According to NASA there's a good chance they occur naturally.
The team found adenine and guanine, which are components of DNA called nucleobases, as well as hypoxanthine and xanthine. ...Hypoxanthine and xanthine are not found in DNA, but are used in other biological processes.
Also, in two of the meteorites, the team discovered for the first time trace amounts of three molecules related to nucleobases: purine, 2,6-diaminopurine, and 6,8-diaminopurine; the latter two almost never used in biology. These compounds have the same core molecule as nucleobases but with a structure added or removed. ... "However, if asteroids are behaving like chemical 'factories' cranking out prebiotic material, you would expect them to produce many variants of nucleobases, not just the biological ones, due to the wide variety of ingredients and conditions in each asteroid."
And we've been able to produce them in the lab using non-biological reactions.
Thirdly, the team found these nucleobases -- both the biological and non-biological ones -- were produced in a completely non-biological reaction. "In the lab, an identical suite of nucleobases and nucleobase analogs were generated in non-biological chemical reactions containing hydrogen cyanide, ammonia, and water. This provides a plausible mechanism for their synthesis in the asteroid parent bodies, and supports the notion that they are extraterrestrial," says Callahan.
NASA scientists studying the origin of life have reproduced uracil, cytosine, and thymine, three key components of our hereditary material, in the laboratory. They discovered that an ice sample containing pyrimidine exposed to ultraviolet radiation under space-like conditions produces these essential ingredients of life.
Rather than being a fluke that happened once on Earth, DNA, or at least its building blocks, appear to occur naturally. So another planet would have the same chemical base pairs available for proto-life to produce DNA.
DNA and RNA are very good at what they do: encode the blueprints for an organism very efficiently, accurately enough to ensure stability, but allowing sufficient inaccuracies for evolutionary variations to respond to changes in the environment. It's so good at what it does that despite billions of years of evolution and endless variety no life on Earth does anything else. This implies that even if several competing forms of life arise on another planet, DNA/RNA based life will win.
RNA might be more likely.
Just because the base pairs are there doesn't mean you get DNA. You might get RNA first, known as the RNA World Hypothesis. RNA has many of the properties of DNA which are important to life: it's self-replicating, it can act as a catalyst, and it can make proteins. RNA is more fragile, making it suitable for only simple life, but that's exactly where life starts out.