According to Dharmaranya khanda of Skanda purana, Dharma tirth or Dharmaranya is nothing but the Gokarna kshetra. But, there are other versions too- like the Gautamashrama near Vindhyavasini Sakthipeeth. According to Swarga khanda of Padma purana it is located between Ghazipur and Balia in Uttar pradesh. According to Kurma purana it's on the southern bank of river Mandakini in Uttaranchal. Mahabharata describes it as Kanvashrama of Rajasthan. According to Buddhists it's near Bodhi Gaya of Bihar.
The context you are telling refers to the Gokarnam. Lord Yama Dharma Raja and Dharma devata were blessed by lord Shiva in this place. We in Narmada parikrama tour, after the tour I can post more details on this. If you have any other version please post.
Iam referring to the following context w.r.t Dharma teerth.
Sage Narad continued with the description of various holy places and said--- "A pilgrim must visit Dharma Teerth, which is named after the lord of ďeath--Dharma. Once upon a time Dharmaraj had performed an austere penance at that place this is the reason why it became famous as Dharma Teerth. By visiting Dharma Teerth, a man liberated all his ancestors up to seventh generation. After that a pilgrim should go to Kalap-forest, Saugandhik-forest, Suvarna-Dhumavanti respectively. All the above mentioned holy places are capable of giving salvation."
Your excerpt is from Padma purana, i.e, it is describing the area above Varanasi, between Ghazipur and Balia. But, this story is also narrated in Skanda. Dharma dig a pond here, for his Shiva puja, called Dharma Pushkarin. It is described to be located adjacent to Phullagrama, near South sea, i.e, Gokarnam. Galva maharshi also spent his life here.