After seeing the answer here, I have a feeling that the Indra of the Vedas is not the rain god Indra we have in the Puranas. Do any verses in the Vedas show the Indra mentioned there is the same as the rain-god?
Is Indra of the Vedas the rain god Indra?
Yes, as per Rigveda, Indra of the Vedas is the rain god Indra.
English Translation: Guarded by Ahi stood the thralls of Dāsas, the waters stayed like kine held by the robber. But he, when he had smitten Vṛtra, opened the cave wherein the floods had been imprisoned.
English Translation: I WILL declare the manly deeds of Indra, the first that he achieved, the Thunder-wielder. He slew the Dragon, then disclosed the waters, and cleft the channels of the mountain torrents. He slew the Dragon lying on the mountain: his heavenly bolt of thunder Tvaṣṭar fashioned. Like lowing kine in rapid flow descending the waters glided downward to the ocean. Impetuous as a bull, he chose the Soma and in three sacred beakers drank the juices. Maghavan grasped the thunder for his weapon, and smote to death this firstborn of the dragons.
English Translation: Unclose, our manly Hero, thou for ever bounteous, yonder cloud, For us, thou irresistible.
Note: In most of the Richas of Rigveda, Indra is mentioned as rain god or slayer of Vrita (who blocked the rain). But there are few Richas (like in the link provided in your question) where Indra is mentioned differently, it's because Richas in Rigveda are from different different Sages.