The Kshetrapala god mentioned is Lord Krishna.
Pariyatra mountains are among the mountain ranges which are termed as Kala mountains in the Mahabharata and their mentions are present in Puranas as well. There are several mentions of it in the Mahabharata but it is not mentioned who is the God dwelling on those mountain ranges. To this Harivamsa Purana gives us an answer.
There are two gods staying on the Pariyatra mountains. They are Lord Shiva and Lord Krishna. The reason why they are staying there is explained in the HariVamsa Vishnu Parva Chapter 74
There is a war between Krishna and Indra for the Parijata. Lord Krishna mounted on Garuda fights with Indra mounted on his elephant Airavata. There took place a fierce battle between them. It has become night and they decided to fight in the next morning. Indra stayed at Pushkara and made a cover of the mountains. (He considered the mountain as a protection). Lord Krishna stayed at Pariyatra mountain that night.
Since, the mountain became tender soft like the shoots of black gram, he named the mountain Shanapada and gave boons to the mountain.
(kR^iShNa said) O great mountain! You will be famous as (shANapAda) the soft one like the tender shoots of black gram. As the auspicious upper half of the mountain himAlaya, you will be auspicious with your merit.
O the best among mountains! As you become abundant with many varieties of wonderful animals, you will compete with the mountain meru.
Then he called Ganga there and invoked Lord Rudra there. Lord Rudra accompanied with Uma and the ganas arrived there. Lord Krishna worshipped Shiva with Bilva leaves and the water of Ganga. Then Lord Shiva pleased with the worship, he said thus:
O the best among deva-s! O the one fixed in dharma! Those who praise me with devotion, with the hymn with which you praised me, will become observers of dharma. O the one without any sin! O lord of lords! O lord! I will remain here by the name of the lord of bilva and water (bilvodakeshvara) as you installed me. According to me, all requests made from here will become fruitful. O keshava! O janArdana! The wise person who worships me with devotion, fasting for three nights, will attain the worlds desired by him. Here, on this land, ga~NgA will flow by the name avindhyA. The baths taken in the river, with mantras related to ga~NgA, will be equal to the baths taken in ga~NgA. O janArdana! Here, under the earth, there is a city named shaTpuraM, a city of dAnava-s, where valiant, highly powerful dAnava-s reside. Those wicked daitya-s are like thorns for the world and gods. O govinda (kR^iShNa)! They reside on the great mountain, concealed. O the one without any sin! They can not be killed by the gods due to a boon given by brahma. But O keshava! As you are a human being, you can kill them. O the ruler of men (O janamejaya!) (vaishampAyana continued) Saying this, shiva disappeared from there, embracing the great soul, vAsudeva (kR^iShNa).
After Lord Shiva disappeared, the night was over and it was morning. Then Lord Krishna said the following words to the mountain Pariyatra
O the best among mountains! Under you great asura-s are residing who can not be killed by gods due to a boon received from brahma long ago. I have blocked the exit of those powerful daitya-s. They will not be able to come out. They will perish there as the exit is blocked by my order. O great mountain! I will always be present on you. I shall remain here pressing those terrible daitya-s. O the best among mountains! Climbing up the mountain, and seeing my idol will yield the eternal result of giving away a thousand cows. Those who make my idol with stones taken from you and worship daily with devotion shall eventually attain my path. In this way, kR^iShNa who gives boons, blessed the mountain with a boon. Since then, one who does not suffer a fall (kR^iShNa), is present on that mountain, always.
Now, we know Shiva and Keshava both stay on Pariyatra mountain ranges. Who is the Kshetrapala God? A Kshetra pala god means a Guardian of a place and protects the place from something dangerous. According to the boon given by Lord Krishna to the mountain, he is the one who promised that he will stay there and suppresses the danavas present in the city named shaTpuraM from entering into this world. So, he should be the one the Kshetrapala mentioned in the excerpt of the Braihaspati Sutras.