So it seems like the reason that some people may conclude that this prayer is written to unbelievers is because of the way verse 16 and 17 are rendered in the NIV:
16 I pray that out of his glorious riches he may strengthen you with power through his Spirit in your inner being, 17 so that Christ may dwell in your hearts through faith. And I pray that you, being rooted and established in love,
...And being a careful reader one might ask, "Why would Paul be praying that Christ dwell in the heart of Christians if Christ is already in their heart?"
...And upon asking, one might conclude, "Well, he wouldn't, therefore he must be praying on behalf of not Christians who have yet to have Christ in their heart."
This is an understandable line of critical reasoning based on the evidence provided in the NIV, however, the NIV translation in verse 14-17 kinda distorts Paul's message by artificially chopping up what might to some seem like an awkward long run-on sentence in English.
While no translation is perfect, however, some translations, like the ESV do a comparably better job at rendering Paul's flow of thought through these verses:
14 For this reason I kneel before the Father, 15 from whom every family in heaven and on the earth is named. 16 I pray that according to the wealth of his glory he may grant you to be strengthened with power through his Spirit in the inner person, 17 that Christ may dwell in your hearts through faith, so that, because you have been rooted and grounded in love, 18 you may be able to comprehend with all the saints what is the breadth and length and height and depth, 19 and thus to know the love of Christ that surpasses knowledge, so that you may be filled up to all the fullness of God. -Ephesians 3:14-19 (ESV)
Notice how, in verse 17, instead of the sentence ending with Christ dwelling your hearts through faith, Paul is actually praying that they have the strength for Christ dwelling in their heart through faith in such a way that they are rooted and grounded in love, and are able to possess with all the saints the full measure of Christ's love so that they may be filled completely with all of the fullness of God.
Paul isn't praying for people who never had the spirit Christ in their heart to have him, but for those who have him, to be strengthened so that the spirit of Christ dwells in their hearts completely so that they are filled to the absolute maximum extent possible with Christ's love - with everything God has to fill man's heart with.