This is getting a bit much for my very limited Chinese, hopefully someone more knowledgeable is around. FYI, “preparing” a text merely refers to getting the digital file in order, and doesn’t involve any understanding!
This phrase in Chinese parallels the Pali at SN 12.20, which is:
Uppādā vā tathāgatānaṃ anuppādā vā tathāgatānaṃ, ṭhitāva sā dhātu dhammaṭṭhitatā dhammaniyāmatā idappaccayatā
Focusing on the main section that you’re interested in, with a word-by-word analysis:
ṭhitāva sā dhātu dhammaṭṭhitatā dhammaniyāmatā idappaccayatā
that property indeed stands, that stability of principle, that lawfulness of principle, specific conditionality.
Luckily we have a Sanskrit version of the same text at SF 163. In this case, the Sanskrit text is very likely to stem from the same, or very similar, tradition as the Chinese translation, and this passage bears this out:
sthitā eveyaṃ dharmatā dharmasthitaye dhātuḥ
That principle indeed stands, that element of stability of principle
My Sanskrit grammar is not very good, so I’m not entirely confident about the syntax here, but it’s something like this.
The relation between the Sanskrit and Chinese is thus very close:
sthitā eveyaṃ dharmatā dharmasthitaye dhātuḥ
此法常住, 法住 法界
Both versions lack, in this passage, anything corresponding to the niyāma of the Pali, or to idapaccayatā at the end. In addition, they do not have dhātu near the beginning of the phrase, but at the end.
The only difference between the Sanskrit and Chinese is that the Chinese inserts an extra 法, which appears, as you said to represent dharmadhātu, a term not found in the Sanskrit. So either the Sanskrit text on which the Chinese translation was based differed in this word, or it was added by the translator, perhaps for clarity. The terms dharma and dhātu have almost identical meanings in the EBTs, and the notion of dharmadhātu as found in the Mahayana was as yet unknown when the Sanskrit text was formed; whether it may have influenced the Chinese translator, I could not say.
We should not draw any doctrinal conclusions from these variations, however. While the Sanskrit text lacks the terms niyāma and idapaccayatā here, in the body of the passage, it does include them a little later, when summing up the teaching by giving a long list of synonyms for pratītyasamutpāda:
iti yātra dharmatā dharmasthititā dharmaniyāmatā dharmayathātathā avitathatā ananyathā bhūtaṃ satyatā tattvatā yāthātathā aviparītatā aviparyastatā idaṃpratyayatā pratītyasamutpādānulomatā ayam ucyate pratītyasamutpādaḥ
Thus it seems clear that the differences between the texts are merely verbal.