This verse is part of first mandala, 32 sukta, verse 10. This Sukta talks about manly deeds of Indra and how he achieved, the "Thunder weilder" by killing a Asura by name "vṛtrasura". As said in first verse of same sukta:
“I declare the former valorous deeds of Indra, which the thunderer has achieved; he clove the cloud; he cast the waters down (to earth); he broke (a way) for the torrents of the mountain.” ||1||
...
“With his vast destroying thunderbolt, Indra struck the darkling mutilated Vṛtra; as the trunks of trees are felled by the axe, so lies Ahi prostrate on the earth.” ||5||
“The arrogant Vṛtra, as if unequaled, defied Indra, the mighty hero, the destroyer of many, the scatterer of foes; he has not escaped the contact of the fate (Indra's) enemies. The foe of Indra has crushed the (banks of the) rivers.” ||6||
So, now it is clear Vṛtra was a Asura. Now What exactly does "vṛtrasya niṇyaṃ" refer to? To answer your question, we should read the verse correctly.
atiṣṭhantīnām aniveśanānāṃ kāṣṭhānām madhye nihitaṃ śarīram |
vṛtrasya niṇyaṃ vi caranty āpo dīrghaṃ tama āśayad indraśatruḥ ||
Where shariram means body which has to be connected to the next line vṛtrasya niṇyaṃ. vṛtrasya means "vṛtra's" and "niṇyaṃ" means hidden/secret. Simply saying "vṛtra's hidden" may not sound correct, but if we say "vṛtra's hidden body", it would make sense as after Indra kills him, the water flows over him and makes his body hidden.
I found more relatable translation from sri-aurbindo's rigveda mandala 1, sukta 32:
The hidden body of Vritra laid in the midst of courses of the not standing ones, not stopping – the Waters spread widely; {he,} to whom Indra is enemy, lay in the long darkness.
Hope this helps.