What does "alright" mean when it's at the end of a sentence?

a. Life has no meaning alright.

What does "alright" mean in the sentence above? I can't find it in the dictionary!

Well it is listed in several dictionaries here, but in fairness not all of them list the sense it is used in in this case, so I could see how you might have missed it.

Its a colloquial use (and so not found everywhere, not considered correct by everyone, and not appropriate for formal use) that serves to emphasise a previous assertion.

You can consider it equivalent to "without doubt", indubitably, surely, etc. Many people whose dialect is such that they don't use it have another expression they do use, like "for sure".

As William points out in a comment, it would be common to set off the interjection with a comma:

Life has no meaning, alright.

Which in itself helps show that "life has no meaning" stands as a clause of its own.

In the context you present, the 'alright' could connote two somewhat different perspectives, depending on how the sentence is spoken:

• When the utterance is emphatic, it is an expression of irritability — the equivalent of something like "Life has no meaning, as any fool can see!".

• Spoken in more measured tones, it sounds like an acknowledgement of the correctness of an assertion made by the speaker's interlocutor: "Indeed, life has no meaning!".