The word God (θεός - Theos) does not actually appear at all in the Greek text either verse 15 or either of the verses before or after it. The literal Greek of verse 15 probably reads closer to something like the NKJV:
14...that you keep [this] commandment without spot, blameless until our Lord Jesus Christ’s appearing,
15which He will manifest in His own time, [He who is] the blessed and only Potentate, the King of kings and Lord of lords
It may be that the NIV translators were troubled by verse 16:
who alone has immortality, dwelling in unapproachable light, whom no man has seen or can see ... (NKJV)
leading them to conclude that the King of kings and Lord of lords had to refer to God the Father and not God the Son, who had become Incarnate.
Apparently this was somewhat ambiguous even for Greek readers. John Chrysostom, a Byzantine Greek, wrote in his 4th century commentary on this verse:
Of whom are these things said? Of the Father, or of the Son? Of the
Son, undoubtedly: and it is said for the consolation of Timothy, that
he may not fear nor stand in awe of the kings of the earth.
He goes on to explain, however:
But he says only [who alone] either in contradistinction to men,
or because He was unoriginated, or as we sometimes speak of a man whom
we wish to extol.
Who only hath immortality. What then? hath not the Son immortality? Is He not immortality itself? How should not He, who is of the same
substance with the Father, have immortality?
Dwelling in the light which no man can approach unto. Is He then Himself one Light, and is there another in which He dwells? is He then
circumscribed by place? Think not of it. By this expression is
represented the Incomprehensibleness of the Divine Nature. Thus he
speaks of God, in the best way he is able. Observe, how when the
tongue would utter something great, it fails in power.
Whom no man hath seen nor can see. As indeed [i.e. with respect to His Divine Nature] no one hath seen the Son, nor can see Him.
Gregory of Nyssa (4th c.) explained this passage in a similar way in his arguments against Eunomius, head of an extreme 4th century Arian sect that denied the divinity of Christ:
“God,” he [Eunomius] says, “Who is without beginning, eternally,
without end, alone.” Once more understand, ye simple ones, as
Solomon says, his subtlety [Prov 8:5 LXX], lest haply ye be deceived and fall
headlong into the denial of the Godhead of the Only-begotten Son. That
is without end which admits not of death and decay: that, likewise, is
called everlasting which is not only for a time. That, therefore,
which is neither everlasting nor without end is surely seen in the
nature which is perishable and mortal. Accordingly he who predicates
“unendingness” of the one and only God, and does not include the Son
in the assertion of “unendingness” and “eternity,” maintains by such a
proposition, that He Whom he thus contrasts with the eternal and
unending is perishable and temporary. But we, even when we are told
that God only hath immortality, understand by immortality the
Son. For life is immortality, and the Lord is that life, Who said, I
am the Life [John 14:6]. And if He be said to dwell in the light that no man can
approach unto, again we make no difficulty in understanding that
the true Light, unapproachable by falsehood, is the Only-begotten, in
Whom we learn from the Truth itself that the Father is. Of these
opinions let the reader choose the more devout, whether we are to
think of the Only-begotten in a manner worthy of the Godhead, or to
call Him, as heresy prescribes, perishable and temporary (Against Eunomius II.4)
Thus, I think, these writings from antiquity show that the interpretation of the NIV may be technically correct, but it may not perhaps be the way the verse was understood by "mainstream" Christians in the first few centuries.