No, at first glance - but maybe
This is an interesting question.
So, as is mentioned, Magic Missile requires the target to be a creature. It also has a further requirement, that it will hit unerringly even if the target "has less than total cover or total concealment" (PHB p.251). By extension, you need to be able to perceive the creature.
There is a suggestion that you may be able to "see" Living Darkness as long as you are an lit space. The contrast with its surroundings is how you "see" it, even though you can't literally see it. As a DM I would rule this works in the same way as you would perceive a Shadow. You can target non-corporeal creatures such as a Shadow which is " sentient darkness hating life and light with equal fervor. [...] a Shadow can be difficult to see in dark and gloomy areas but stands out starkly in brightly illuminated places" (MM p.221).
In the various entries of Living Spells of Monster Manual III all the examples are identified as Oozes.
It all comes down what the DM declares:
- if Living Darkness counts as a creature/ooze, then Magic Missile can indeed target it, as long as you can distinguish it from its surroundings - i.e. create a contrast, like you would with a Shadow;
- if it is not a "creature" per se, then *Magic Missile" cannot target it.
We can also look for clues at other spells that are not an "Ooze", such as an Unseen Servant (PHB pp.297-298) for instance. It is not a "creature" per se; rather, it is described as a "magical force" by Jeremy Crawford. Looking ahead, in 5e it is described as force as well and it has a mere 1 HP; it can also be damaged and if it takes one damage the spell ends. So, there is a continuity in this theme of a "(magical) force".
Arguably, Living Darkness could be targeted even if the DM considers it a force, but probably not by Maggic Missile.
That is not to say that there aren't any other spells which could target a non-creature, non-object, Living Spell (i.e. a force).
For instance, the Sanctified spell Hammer of Righteousness from the "Book of Exalted Deeds* is an interesting case. It has a similar flavour to Magic Missile in that it "strikes unerringly". It also requires you to be able to perceive the target.
A great warhammer of positive energy springs into existence, launches towards a target that you can see within the range of the spell, and strikes unerringly. [...] The hammer is considered a force effect and has no miss chance when striking an incorporeal target.
So, although it is unlikely that Magic Missile is able to target a magical force version of Living Darkness, it maybe possible to target it with other spells, such as Hammer of Righteousness - so long as you are able to differentiate it from its surroundings. If it is hidden in other forms of darkness, these would need to be dealt with first to create a contrast.
I think the DM ought to have the final ruling on this, but this is how I would... "see it".
Failing all of this, for problems with pesky Forces, call Yoda and he'll sort it out!