kbtonkin,
First, the minimum yield strength requirement for grade 550X is 550 MPa, as stated in Table 4 of SAE J2340. I am not sure where you see the number 586.
Second, the reason there is a limited requirement for chemical composition is because this standard was specifically created to define performance criteria (strength, elongation) instead of tightly controlled chemical composition limits. These HSLA grades typically have C contents of ~ 0.06-0.10, Mn of ~ 1.00-1.5, and small additions of V, Nb, or Ti (around 0.05-0.10). All number are in mass percent.
Third, you can find more information from suppliers like US Steel, ISG, AK Steel, etc. Most of the steel suppliers reference ASTM standards like A 1011, but the products are essentially the same.