It is not known whether it is his actual eye, but in the scene when the MoM tells Luxu about the gazing eye in the No Name, the MoM says ''my eye, to be exact'', Luxu says ''Ew'' and the MoM replies ''You think that's gross, do you?''
That pretty much implies it is his actual eye, but knowing the MoM's personality he could be joking or exaggerating to startle Luxu for his own amusement. There is the possibility that his ''eye'' could mean not his biological eyeball, but that he somehow transferred the sight of one of his eyes to an artificial eye encased in the keyblade. Xehanort was able to track Sora through the X in his DDD clothes, so the Master transferring his sight to an eye in a keyblade doesn't sound so farfetched.
The eyes on the other keyblades haven't been explained.
Same for the Soul Eater weapons which are not keyblades (except Riku's after becoming the Way to Dawn).
Apparently the only eyed keyblade the MoM can see through is the No Name, probably the other eyes are just for decoration, to make these keyblades look more dark and intimidating. Maybe they were inspired by the original gazing eye, but that would raise more questions, like who made them and how did they know about the eye. I hope we get some explanations eventually, but I'm not counting on it.
There's also the fact that keyblades change its shape with different keychains. Sora's defaul keyblade has no eye, but End of Pain does. Riku's Way to Dawn has an eye, but every other keychain he can equip in DDD (except End of Pain) doesn't have it. Terra's Earthshaker doesn't have it, but Chaos Ripper does. Void Gear is a black and white version of Vanitas's Quid Vacuo and has the eye.
I wonder if this means that the MoM put the eye on the keychain instead of the actual keyblade or his eye is present in that keyblade no matter what keychain it has. Young Xehanort's version in DDD also had the eye.