Anything caught in the net counts as fish.

Literal

Net [at-に] caught thing [topic-は] whatever fish is.

何でも ('anything, whatever') is the universal-affirmative indefinite — 何 + でも. The overall meaning is proverbial: once something is caught, it's treated as fish regardless of what it actually is. The relative clause 網にかかったもの ('the thing that got caught in the net') modifies もの, serving as the topic of the predicate. かかる ('to get caught, to get hooked on') is a common intransitive verb for things snagged or stuck.