"Retiring" as a verbal noun (a 'gerund') is only used in the sense of "the process of stopping work", whereas "retirement" is used more often of the resulting state.
So when you talking about the act
I'm thinking of retiring next year.
is normal.
I'm thinking of retirement next year.
is possible, but to me means that you are thinking of the state of being retired, not of the process of retiring.
But
I'm going to enjoy my retirement.
You can't use "retiring" there.
Clearly this isn't the whole story, because it would imply that, in your example, we would say "the legal age of retiring". But, while this is possible, it is not natural. I think set phrases all use "retirement": "age of retirement"; "retirement party"; "retirement present".
As others have pointed out "retiring" is also a participle and an adjective.
Best Answer
English is a quirky language because it's primarily a mix of two separate linguistic families -- those languages that come from the Latin, particularly Old French, and those languages that come from the Germanic, particularly Anglo-Saxon. Sometimes two words from each of these branches look and sound very similar, but stem from completely different roots.
Such is the case with evil and devil. As you say, devil comes from the Old English deofol, from the Latin diabolus, which in turn derives from the Greek diabolos. Because of its use in the Church, it's a word that has permeated many European languages, in much the same form, Portuguese: diabo, German: Teufel, Danish: djævel, Dutch: duivel, and so on.
Evil however is from the Old English yfel derived from the Proto-Germanic ubilaz. This is why the languages that derive from the same source have similar words: Dutch: onheil, German: übel, Danish/Norwegian/Swedish: ond/ont, and so on.
Meanwhile the languages in the Latin branch all have words for evil that derive from malus: Spanish/French/Portuguese: mal, Italian: male, and so on, as well as those English words that come from that branch: maleficent, malevolent, malediction, malignant,, and so on.
Long answer short: it's a coincidence. But a fun one, nevertheless.