I would like to highlight that adultery, in this context, is only applicable under sharia law, which is applicable in the northern parts of the country. At least 19 states, in the northern part of the country, apply sharia law.
Yes, of course, it is heavily skewed against women. The case that brought Avocats sans frontières France to Nigeria was actually one of such cases, that of a woman who was sentenced to death by stoning for adultery, so yes, that's the reality.