etymology - Preservation of the en- prefix form of Latin negative prefix in-, in enemy & enmity

Short answer: entire.

Long answer:

The two Latin prefixes in-: negative and prepositional

There are two Latin prefixes that have the same form in- (or im- before p,b, or m; ir- before r, and il- before l). One of them has a negative meaning (it is cognate to and has a similar meaning to the English negative prefix un-). Examples of words with this suffix: invalid, immature, irrelevant, illiterate. The other has a vague but generally prepositional meaning, as it was derived from the Latin preposition in (which is cognate to and has a similar meaning to the English preposition in). Examples of words with this suffix: incident, impulse, irritate, illustrate.

There are many words in English that start with en- or em- derived from the Latin prepositional prefix in- (such as envy, endure and embrace).

However, your question is about the negative prefix in particular.

Development in French of the Latin negative prefix in-

The change of Latin in- to French en- is in accordance with the regular sound change of Latin short /i/ to Proto Western Romance /e/ (shown in a table on this Wikipedia page). However, it seems that in general, negative en- ended up being changed back to in- (in both French and English). As your quote says, in general, the negative meaning of en- is not obvious in the words that retained the prefix. I found a description of this change with some examples here: Principles of English Etymology: The foreign element, by Walter William Skeat.

I don't know why in- ended up being more common than en- in French, despite not following the normal laws of sound change. It may be due to the influence of Latin spelling. French has a lot of learned words that do not show all of the usual sound changes from Latin. This is particularly common for adjectives; for example, the corresponding adjective to the noun école "school" is scolaire. (A somewhat comparable phenomenon in English is "collateral adjectives" such as cow and bovine.)

If French ended up with more words borrowed from Latin with in- than words inherited from Latin with en-, that might have been a reason why speakers gradually regularized the words starting with en- to make them have the more common, synonymous prefix in-.

Examples of negative en- in English: enemy, enmity, entire

I found only one example in Modern English besides enemy and enmity: entire, which comes from Latin integrum (meaning "whole," compositionally from "untouched"). I learned of this example from W. H. H. Kelke's "An Epitome of English Grammar For the Use of Students, Adapted to the London Matriculation Course and Similar Examinations."

Kelke also mentions enfecte, used by Chaucer as a spelling of "infect." The normal verb infect seems to come from the Latin verb inficio "to dye, stain, poison" which has the prepositional prefix rather than the negative prefix. However, there apparently was a Latin adjective infectus which Wiktionary defines as "not done, unfinished; impossible" and which has the negative prefix. If Chaucer's "enfecte" is in fact an example of the negative prefix "en-," as Kelke says, I guess it must descend from this Latin word.

Examples of negative en- in French and Anglo-French

On the French side, one more word with en- from Latin negative in- is enfant, which compositionally comes from "not speaking." In Modern English, this word has become infant, but according to the Oxford English Dictionary spellings like enfaunt, enfant used to be used. The Modern French word, which retains the spelling with en-, has been borrowed into English more recently in phrases like enfant terrible.

In addition, Skeat lists some Anglo-French forms with negative en-: enferme "infirm" and enfermité "infirmity." However, the equivalent words in modern French are spelled with in-: infirme and infirmité.