The New Mexico Territory consisted primarily of present day New Mexico and Arizona. Consider the following: Arizona Ordinance of Secession.
Arizona, which at that time was the Southern portion of both Arizona and New Mexico, wished to join the Confederacy. Hmmm. They didn't even mention slavery. How can that be?
Two things jumped out at me. First, was the use of the name "Arizona Territory." Under the Union government, Arizona Territory did not exist until 1863. Your document is dated March 11, 1861. The meeting place is shown as La Mesilla. Present-day Mesilla is near Las Cruces, New Mexico. The next-to-last clause indicates the New Mexicans (many of whom were former Texans) were responsible for the document. So your identification of the southern portions of both present-day states is correct.
The second thing is that Article IV, Section 3, Clause 3, of the Confederate Constitution of March 11, 1861, made it clear that slavery was to be legal in territories outside of the confederate states:
"In all such territory the institution of negro slavery, as it now exists in the Confederate States, shall be recognized and protected be Congress and by the Territorial government; and the inhabitants of the several Confederate States and Territories shall have the right to take to such Territory any slaves lawfully held by them in any of the States or Territories of the Confederate States."
The Mesilla Convention need not have mentioned slavery at all for it to be legal therein. I also note that the drafters of the Arizona Ordinance misidentify the Constitution as a treaty. This intellectual myopia was common among many southerners.