Btukfyl

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