Linguists call this a deverbal result noun: a noun referring to the results of its corresponding verb.He cites no authority for this contention. The noun "punishment" is a deverbal noun, but it is not a deverbal result noun (as previously discussed in the comments box here).
Roget's Thesaurus provides the following entry for "punishment":
Definition: penalty(Roget's 21st Century Thesaurus, Third)
Synonyms: abuse, amercement, beating, castigation, chastening, chastisement, comeuppance, confiscation, correction, deprivation, disciplinary action, discipline, forfeit, forfeiture, gallows, hard work, infliction, just desserts, lumps, maltreatment, mortification, mulct, ostracism, pain, penance, proof, punitive measures, purgatory, reparation, retribution, rod, rough treatment, sanction, sequestration, short shrift, slave labor, suffering, torture, trial, unhappiness, victimization, what for
Antonyms: encouragement, exoneration, praise, protection, reward
As you can see, most of the descriptions of "punishment" are of processes, not of results. The punishment may be the beating, whereas the hoped-for result is correction of behavior.
Thus, for example, "eternal punishment" would be similar to "eternal abuse," "eternal amercement," "eternal beating," "eternal castigation," etc. When each of those words is modified by "eternal," what is referred to is the duration of the process, not the duration of the effect. An "eternal beating," is a beating that does not have an end, in contrast to something like an "eternal scar" which would be a scar that would last forever.
So, "punishment," like "walk," is a manner noun, not a "result" noun. Mr. Date quotes from Augustine who says that people wouldn't consider capital punishment as measured primarily by its duration. This is true, but it misses the point. Capital punishment is severe regardless of its duration, because of the kind of punishment it is. But "eternal punishment" is specifically a comment on the duration of the punishment.
The lexical analysis is a little complex (see here and here), but it should be intuitive, particularly when you see the synonyms above.
Punishment describes a manner of treatment, not the result of that treatment. Thus, "punish" is more like "walk" (a manner verb) than "go" (a result verb) - it's more like "wash" (a manner verb) than "clean" (a result verb). It tells you more about the process than about the outcome. But "punish" and "punishment" are about the process.
Therefore, Mr. Date is all wet in his linguistic claim. Linguists may refer to a category of "deverbal result nouns," but Mr. Date has not identified any that treat the noun, "punishment," that way.
P.S. Incidentally, while Mr. Whipps and I advocated for the same side in our respective debates against "conditionalism" (aka annihilationism), our presentations are quite different.