I'm new to Danish as well, so take this with a grain of salt. "isn't going to" is simple future. "does not" is simple present. Now future is usually not marked in Danish, so technically the sentence could imply future? However, it would usually do so by using modal verbs like "vil" - e.g. "Brevet vil ikke skrive sig selv!"
You are right about the simple present and simple future. But right now I'm learning Danish in Denmark and when you use the word 'vil' it actually means 'would like to' instead of 'will'. So you're sentence would actually mean 'The letter would not like to write itself!'.
Others have explained the use of "vil" - simple future without reference to a specific time correctly uses the verb "at ske" so "The letter will not write itself" would be "Brevet skal ikke skrive sig selv".
However "The letter is not going to write itself." would probably be translated as "Brevet kommer ikke at skrive sig selv" (lit. The letter does not come to write itself).