I guess people are getting confused over the meaning and the concept of celibate marriage.
The concept itself is not new in Shari'ah. It's even there in the Qur'an. What is new to many people is the title that it has been given "Celibate Marriage".
How marriage can be celibate?
The main purpose of marriage for most people is to allow the couple to enjoy the person of one another i.e. conjugal rights. But what if the couples were young, were not ready financially, didn't want to lose the opportunity of being together or as it is now in modern life hang out with each other on campus or even off campus without a mahram?
Celibate marriage is a legal marriage which makes the two contracting parties husband and wife. It is the first step of initiating a marriage contract.
All marriages start with a celibate marriage for a certain period of time. One week, two weeks and even months or years…that's what they call it Katbul Kitab (The Establishment of the marriage contract) and some call it engagement period.
During this engagement they are legally married before Allah, Islamic law and before the people as well. It’s not just the type of engagement understood from the English word which means the promise of marriage.
Because of this all the rulings and integrals of marriage contract are to be observed like any other contract.
The difference now is in the consequences of this form. During the Katbul Kitab (engagement) period they have a choice to consummate the marriage soon afterwards or stall that util more convenient time.
If they choose to consummate the marriage i.e. the actual intercourse which all Fuqha' agree on they will be entitled for their rights and commanded to observe their responsibilities.
Rights like housing, providing, living together, obedience of the husband, as well as the Mahr.
If they chose to wait and not consummate the marriage contract i.e. stay under the roof of their own parents, they are still legally a husband and wife but the rights and obligations are still limited until the consummation takes place.
The all the contracting parties are responsible to agree on this and to set a reasonable time for the consummation time i.e. the wedding party.
In the case of celibate marriage the husband is not yet responsible for housing, finances, and so on and her obedience is still to her father in most of her affairs. However, they are still allowed to be together.
In case they choose to consummate the marriage i.e. have an actual intimate relation (intercourse) even without the knowledge of their guardians the celibate marriage is over and the wali has the right to force him to provide for his wife.
What they did of consummating the marriage was not haram, it just changes the status of marriage and the set of rights and obligations.
In this case the husband has no right to keep her in her family's house and then demand obedience. Unless her wali accepts to keep it for a longer time.
Celibate marriage is widely practiced in Muslim countries where the young couple engage (Katbil Kitab) but they don't consummate the marriage until they prepare everything and feel ready to bear the responsibility of marriage.
It’s nothing new in Shari'ah or Fiqh.
Here are the two ayat in the Qur'an regarding a case of marriage that was not consummated (remained celibate) and ended with divorce:
 And if ye divorce them before consummation, but after the fixation of a dower for them, then the half of the dower (is due to them), unless they remit it or (the man's half) is remitted by him in whose hands is the marriage tie; and the remission (of the man's half) is the nearest to righteousness and do not forget liberality between yourselves. For Allah sees well all that ye do.
 O ye who believe! when ye marry believing women, and then divorce them before ye have touched them, no period of 'Iddat have ye to count in respect of them: so give them a present, and set them free in a handsome manner.
(and 'touched them' by the consensus of the Fuqaha means the actual intercourse as an undisputable act of consummation)
From these Ayat we understand that the couple is not yet entitled to their rights and obligations in full terms until they consummate the marriage.
As for inheritance in case of death the two contracting parties become eligible for full right in inheritance at the time of the contract not the consummation of marriage.
Delaying the consummation of marriage from the time it was contracted makes the marriage celibate as long as they all agree on it especially the wali of the bride.
Consummating it quickly is more preferable.
And Allah knows the best.