Thanks for the question. This is a very common statement/excuse.
The first thing one would need to know is whether or not they both profess to have trusted in Christ for salvation. If they are not Christians I would probably deal with them a little differently -- that is, they first need to get saved, and then turn away from their sin. (They don't need to "clean up" so that God can save them; they need to admit their sin and trust in the work of Christ to cleanse them from their sin. See 1 Corinthians 6:9-11.) Living together is sin, however (see Hebrews 13:4). They may need to be shown the passages below to see that they are living in sin.
With this caveat I think I would be inclined to respond in this way:
"You are right in concluding that marriage is, first and foremost, a matter before God. If this is the case, it is very important to make sure that your "marriage" conforms to what God has said about it in His Word. In Malachi chapter 2 God says that a woman is one's wife 'by covenant.' He goes on to say that He hates divorce, which is the breaking of that covenant. Have you made this covenant before God? If so, why would you not make it before men?"
I would also turn to John chapter 4, and the woman at the well. This woman with whom Jesus talked was living with a man, but both she and Jesus agreed that he was not her husband. This surely implies that her relationship, outside marriage, was sin. They were not "married in God's eyes," because Jesus said they weren't. Jesus went on to tell her that she needed to be born again by trusting in Him.
I would also turn to Ephesians chapter 5, where Paul indicates that the relationship of a husband and wife is designed to be a picture of Christ and His bride, the church. God takes our conduct in marriage very seriously because it reflects on Him.
My guess is that people choose not to go through a marriage ceremony because they don't want to make the commitments that a marriage requires or implies. They also think that terminating the relationship can be done without a divorce. In practical and legal terms (at least where I live) they have a common-law marriage, whether they admit it or not.
When God entered into relationship with man, He did so by means of covenants He made with them. There is the Abrahamic Covenant, for example (Genesis 12:1-3), and the Mosaic Covenant (Exodus 20; Deuteronomy 5 -- actually it includes more than that). Now, we live under the New Covenant (Jeremiah 31; Luke 22). It is these covenants that give the believer assurance and confidence that God will keep His word. It was God's covenant promises with the patriarchs that was the basis for Moses' appeal to God for Israel (Exodus 32:13).
I'm certain that your relatives' practice in this regard is totally inconsistent with their practice in other areas. Would they purchase or sell a home without any legal documents or commitments? Would they expect a bank to loan them money without the proper paperwork? No. They just want to avoid any commitments.
I will pray that God will give you words of wisdom to speak to your friends.