No just being loyal is not enough.One has to avoid his wife on the period days and few other forbidden days too.
If a husband does that then many scriptures declare him to be as good as a celibate.
Here i am quoting from Manu Smriti:
Manu Smriti 3.50. He who avoids women on the six forbidden nights and on
eight others, is (equal in chastity to) a student, in whichever order
he may live.
Here by student is meant a Brahmachari(celibate) who has to maintain celibacy as a rule.
Thanks @sv for adding that Linga Purana page in the question.That same page also says :
Therefore one should practice detachment mentally verbally and
physically.Abstention from sexual intercourse ,except during the
prescribed period after menstruation is believed to be celibacy for the
So,just being loyal to one's wife is not enough although it is absolutely necessary.There are few prescribed days and few forbidden days.On the forbidden days the wife should be avoided as well,and, it's only then that the husband is equal to a celibate.
NOTE-That one's wife is to be avoided on period days is mentioned in many Texts.I'll try to update my answer with them.
1) From Sadachara Varnan in Brahma Purana:
....never sleep during day time, much less unite with wife; rajaswala
women should observe four nights of menses and observance of five
nights would assure Purushatwa in next birth; in any case, observing
aloofness from husband for five nights would be recommended;
2) From Parshara Smriti:
- On the first day that the blood begins to flow, the woman is comparable to a female Chandala ; on the second, she is like a
Brahmanicide ; on the third, she may be likened to a washerwoman. On
the fourth day, * however, she is entirely pure.
[ Madhava says that
the comparisons imply this, — as great a sin will be incurred by
having intercourse with her on those particular days, as would be
incurred by having intercourse with the females is compared to.]
Similarly,Yajnavalkya Smriti,Chapter 1,Verse 79 says:
Sixteen days or nights commencing with the day of menses are the
menstrual period of the womankind ; of them one should know his wife
on the night of an even day such as, the fourth,the sixth or the
eighth , night.This is Brahmacharryam.On the other hand,one should
avoid parva days, and the first four days of menses.
From Vyasa Smriti:
The first four nights of the period should be avoided as Parva days,
as well as those marked by the asterisms called Revati, Pitraksha and
Rakshasa. Fecundation should take place on each even night during the
menstrual peroid alone. (43)
Even the vow of a Brahmacharin, who visits his wife during her
menstrual period, is not vitiated by so doing. Even he, who does not
know any other woman, commits no sin by going unto his own wife during
her menstrual period according to the natural inclinations of his
mind. (45)(Vyasa Smriti,Chapter 2,verses 43,45)
So,the point i made at the start of my answer is repeated in almost all Scriptures.Cohabiting with one's wife ,except on the given prohibited days,is equivalent to maintaining celibacy.
Now,if your real question is "how" then that can't be answered from Scriptures.
BTW your original question was asking Is being loyal to one's wife equivalent to celibacy if so how? But after the Edit it appears that you are only asking about the "How" part.So, i addressed your "Is" part quite well but as i have said the "How" part can't be answered from Scriptures.