Leaving aside the very real issues of straight, cis-gendered privilege in this argument...
All contests have stipulations and requirements. Lambda Literary Foundation has the right to make whatever stipulation and requirement they want to. This is not unprecedented. Many minority groups have awards and scholarships and other category-based recognition in order to nurture members of their minority who lack the opportunities that many members of the majority have at their disposal.
Narrowing the eligibility for their award does not mean that Lambda Literary Foundation is telling you what you can or cannot write. They do not control that, and I doubt they would attempt to control that.
Non-US citizens cannot enter the Miss America pageant. Cis-gendered males cannot enter the Miss America pageant. This is not saying that all Americans discriminate against non-US citizens or males or married women or any other requirement of pageant eligibility. This is just saying that this particular contest has chosen its guidelines, and that is their prerogative.