Gfrktyl

In his book of Raja Yoga, Vivekananda says the following

Lines in chapter II

Râja-Yoga is divided into eight steps. The first is Yama —
non-killing, truthfulness, non-stealing, continence, and non-receiving
of any gifts. Next is Niyama — cleanliness, contentment, austerity,
study, and self-surrender to God. Then comes Âsana, or posture;
Prânâyâma, or control of Prâna; Pratyâhâra, or restraint of the senses
from their objects; Dhâranâ, or fixing the mind on a spot; Dhyâna, or
meditation; and Samâdhi, or superconsciousness. The Yama and Niyama,
as we see, are moral trainings; without these as the basis no practice
of Yoga will succeed. As these two become established, the Yogi will
begin to realise the fruits of his practice; without these it will
never bear fruit. A Yogi must not think of injuring anyone, by
thought, word, or deed. Mercy shall not be for men alone, but shall go
beyond, and embrace the whole world.

Lines in Chapter V

There must be perfect chastity in thought, word, and deed; without it
the practice of Raja-Yoga is dangerous, and may lead to insanity. If
people practice Raja-Yoga and at the same time lead an impure life,
how can they expect to become Yogis?

He didn't explicitly tell to abstain from sex. What is meant by chastity in this context? If a person is married, is he eligible to practice it in-spite of his participation in intimate activities?

See the following Hatha Yoga Pradipika verse:

Brahmacharyaratasyaiva nityam hitamitasinah
Mandaladdrsyate siddhih kundalyabhyasayoghinah||

Only one who delights in the life of celibate (brahmacharin), and
always conforms to a moderate and salutary diet, and who practices
Yoga in the form of stimulating Kundalini approaches Siddhi within
forty days

So, maintaining Brahmacharya is essential to get success in any form Yoga. Obviously married persons can practice Yoga if they follow the rule of celibacy.

The Adi Yogi (Lord Shiva) himself is married.

However, note also that for a householder "being a celibate" has a different meaning. See the Yajnavalkya Smriti verse given in this answer

Yes, married persons are eligible to practice any Yoga through which they can enjoy divine bliss. Yogis like Lahiri Mahasaya (disciple of Mahavatar Babaji) or Sri Yukteswar Giri (Guru of Paramahansa Yogananda) or Sri Ramakrishna Paramahansa (Guru of Swami Vivekananda) were all married.

Autobiography of a Yogi / Chapter 31: An Interview with the Sacred Mother:

On one occasion Trailanga Swami, forsaking his usual silence, honored Lahiri Mahasaya very pointedly in public. A Benares disciple objected.

"Sir," he said, "why do you, a swami and a renunciate, show such respect to a householder?"

"My son," Trailanga replied, "Lahiri Mahasaya is like a divine kitten, remaining wherever the Cosmic Mother has placed him. While dutifully playing the part of a worldly man, he has received that perfect self-realization for which I have renounced even my loincloth!"

Chapter 34: Materializing a Palace in the Himalaya:

Mahavatar Babaji to Lahiri Mahasaya

A deep purpose underlay the fact that you did not meet me this time until you were already a married man, with modest business responsibilities. You must put aside your thoughts of joining our secret band in the Himalayas; your life lies in the crowded marts, serving as an example of the ideal yogi-householder.

The cries of many bewildered worldly men and women have not fallen unheard on the ears of the Great Ones, he went on. You have been chosen to bring spiritual solace through Kriya Yoga to numerous earnest seekers. The millions who are encumbered by family ties and heavy worldly duties will take new heart from you, a householder like themselves. You must guide them to see that the highest yogic attainments are not barred to the family man. Even in the world, the yogi who faithfully discharges his responsibilities, without personal motive or attachment, treads the sure path of enlightenment.

No necessity compels you to leave the world, for inwardly you have already sundered its every karmic tie. Not of this world, you must yet be in it. Many years still remain during which you must conscientiously fulfill your family, business, civic, and spiritual duties. A sweet new breath of divine hope will penetrate the arid hearts of worldly men. From your balanced life, they will understand that liberation is dependent on inner, rather than outer, renunciations.

Gospel of Sri Ramakrishna / Volume 1 / Rules for Householders and Monks:

Therefore when the youngsters come here I ask them whether they have anyone at home. (To Mahima) Why should householders renounce the world? What great troubles the wandering monks pass through! The wife of a certain man said to him: 'You want to renounce the world? Why? You will have to beg morsels from eight different homes. But here you get all your food at once place. Isn't that nice?'

"Wandering monks, while searching for a sadavrata,5 may have to go six miles out of their way. I have seen them travelling along the regular road after their pilgrimage to Puri and making a detour to find an eating-place.

"You are leading a householder's life. That is very good. It is like fighting from a fort. There are many disadvantages in fighting in an open field. So many dangers, too. Bullets may hit you.

"But one should spend some time in solitude and attain Knowledge. Then one can lead the life of a householder. Janaka lived in the world after attaining Knowledge. When you have gained it, you may live anywhere. Then nothing matters.