It’s perfectly normal speech; the zero article is often used in this manner. One oft-seen example is the phrase man against man – which is considered a form of literary conflict – but the expression may be found elsewhere as well:
Any violence on the part of man against man or man against nature was a violation of Thoreau's pantheistic views.
(E. A. Moehle - 1972)
The phrase can be used for other living beings, also, such as in the opening sentence of a 2014 LA Times article:
Across the southeastern United States a battle is raging – ant against ant.
I suppose the fragment could be reworded in a couple ways, and still be grammatical:
- Where cells fight cells
- Where a cell fights a cell
- Where cells fight against each other
- Where cells fight one-on-one
But the original has a concise and gritty tone that I think the scriptwriter probably wanted to include.