So this is a definition for "life" only

Precisely.

How many of its own life functions must a parasite be able to perform once removed from the host in order for it to be considered alive after removal from the host?

As the definition says. It must demonstrate non-equilibrium chemistry and must be self-sustaining. Again, 'simple forms of energy' is relative, so I agree that there's some fuzziness here. However, if you look at the extreme complexity of the chemical processes of life (dna, ribosomes, proteins, etc.) and compare that to what most life consumes (sugars, minerals, etc.) there is no ambiguity. It's quite clear that there's a difference.