I suppose you could argue that there's a sense in which the term "decay" can be applied to rocks, but it still isn't biological decay.
Of course it is not "biological" decay. Because rocks aren't alive. But they are not not alive because they don't decay. If life was defined by
only the fact of decay then rocks would be alive.
If you say it is only an analogy then you are assuming that rocks can't biologically decay because they aren't alive. That is circular. The issue is exactly one of separating the biological from the non-biological. The point is you can't use "decay" to do that.
Only when you have some independent definition of what makes something biological can you say that rocks don't biologically decay.