Eyes of the Dark, a feature from the Shadow Magic (Sorcerer) class, allows the PC to cast darkness by expending a spell slot, or 2 sorcery points. If I cast the spell in that way (either expending a spell slot or 2 sorcery points) am I allowed to cast another spell that requires Concentration?
No, you can't cast and maintain another concentration spell at the same time
When you reach 3rd level in this class, you learn the darkness spell, which doesn't count against your number of sorcerer spells known. In addition, you can cast it by spending 2 sorcery points or by expending a spell slot. If you cast it with sorcery points, you can see through the darkness created by the spell.
Nothing in that indicates that the normal rule of concentrating on only one spell at a time is suspended when you cast the darkness spell by either method. If you cast another concentration spell, your concentration on the darkness spell will end.