Solution 1:

Devotement is an outdated, less common variant of devotion:

  • The action of devoting, or fact of being devoted; devotion, dedication.
    • 1604 Shakes. Oth. ii. iii. 322 He hath deuoted, and giuen vp himselfe to the Contemplation, marke, and deuotement of her parts and Graces.
    • 1852 Wayland Mem. Judson (1853) i 29 His own personal devotement to the missionary cause.

OED

Ngram: devotement vs devotion.

Ngram: devotement.

It origin is probably due to the practice of adding the suffix -ment to verbs to form nouns which starred from the 16th century:

-ment :

  • suffix forming nouns, originally from French and representing Latin -mentum, which was added to verb stems sometimes to represent the result or product of the action. French inserts an -e- between the verbal root and the suffix (as in commenc-e-ment from commenc-er; with verbs in ir, -i- is inserted instead (as in sent-i-ment from sentir).

  • Used with English verb stems from 16c. for example merriment, which also illustrates the habit of turning -y to -i- before this suffix).

(Etymonline)

Devotion (n.) has an older origin:.

  • early 13c., from Old French devocion "devotion, piety," from Latin devotionem (nominative devotio), noun of action from past participle stem of devovere "dedicate by a vow, sacrifice oneself, promise solemnly,"

From which devote (verb)

  • 1580s, from Latin devotus, past participle of devovere (see devotion). Second and third meanings in Johnson's Dictionary (1755) are "to addict, to give up to ill" and "to curse, to execrate; to doom to destruction."

and later (17th century) "devotement".

Solution 2:

It is simply impossible to know why some words survive and others don't, but let's examine the history of these synonyms, which we can do courtesy of the OED.

Devotion is an old word, coming to us from the Old French devocion, ultimately from the Latin devotio. The OED records several senses of he word, the first from 1225, having the connotation of religious devoutness. This follows the Latin meanings which were about religious ceremonies or the taking of vows to devote oneself to virtue. (Latin had others words -- dedere, devovere, dedicare -- to apply to situations of dedicating oneself to things other than the sacred.)

In the 16th century, influenced by more modern Italian and French, devotion started to be used for people, causes, hobbies, and so on. The OED finds 1530 the first use in the sense. In 1604, Shakespeare uses the word devotement in Othello (Act II, Scene iii) where Iago talks about Desdemona:

... Our general's wife is now the general: may say so in this respect, for
that he hath devoted and given up himself to the
contemplation, mark, and devotement of her parts
and graces....

(Well, maybe. That's the First Folio. The Second has denotement. If you won't accept Othello, then the next cite is from 1621.)

There's also another synonym, devoteness, first recorded in 1606.

So the 1600s saw authors turning from devotion and its history of religious connotation to new words useful for secular circumstances as well. With multiple words for both contexts, at some point, people decided to remain devoted to devotion.