Not exactly, this article has some more info
[en.m.wikipedia.org]

Not unexpected from a polytheistic religion. Each household chooses its own patron demigod and you don't adopt a pet deity with the notion that yours is the One True God. When you enter someone else's house you must respect their deity.

Besides, in a polytheistic system, the gods don't inherently compete (though, as in the Greek pantheon, they can be petty and competitive and just generally very human with each other). In polytheism and animism, they are all part of an organic whole. They are more like the Catholic saints than the Catholic deity. The bodhisattva / ascended masters of Buddhism are this way too. Maybe there's some percentage in demoting your deity a couple of pegs so that it's forced to share the mojo with others ...

My understanding of "Hinduism" is that it's not really or "just" a "religion", and more a grab-bag of all kinds of religious, philososophical, and cultural practices from all around that colorful subcontinent.

There are unifying themes, to be sure, which seem to pervade like foundational strata--chief among which, I would posit, is likely the idea that "all paths lead to God." That the notion that "there is no God" can fit completely and cleanly into that framework makes total sense to me, from my impression of "Hindu" thought. There's so much going on that you can take "God" out of it, and there's still worlds of material to work with. And it's totally fine; it's all good. This God, those gods, no God? All good!

I took an intro to philosophy class in which we had a Hindu guest speaker who explained the term "Hindu" is a misnomer. A migrating (conquering?) people came up and said, "All those people over there, on the other side of that river, we're calling them 'Hindus'. It was the Sindu river. Dunno if it was an inability to pronounce or translation error or what else. But I don't think the term originated as a reference to religious identity.

I'm not an Indologist, but I play one on the internet.

That is a very interesting and informative article—thanks for pointing it out.