Is this an appositive?

It is not an appositive, but a supplement. In appositives, the appositive dependent itself could be substituted for the whole noun phrase without changing the meaning much (CaGEL p447). In this case however,

Keep up the great work you're doing, fighting for both animal and human rights.

*Keep up fighting for both animal and human rights

The second is not only grammatically deficient, but also does not mean the same thing as the original.

Supplements do not have a direct grammatical connection to the element they are anchored to, and hence are separated from it by a pause in speech or a comma in writing.

In this case fighitng for... is a supplement to the great work you're doing

Both sentences are grammatical as head noun work is an acceptable anchor for fighting for...

In order for there to be a direct connection between the two, there would have to be a preposition inserted, and the order of the elements in the clause would change.

Keep up the great work of fighting for both animal and human rights that you're doing.