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Yes, it's the same principle that gets you financial advisors who push you into high-fee fund choices that earn them kickbacks. Completely understandable from the PoV of these parties' self-interest, yet entirely contrary to your own self-interest as a customer and investor.

You seem to be confusing "listing" - the stock exchange where a company chooses its stock to trade (i.e. NYSE, AmEx, Nasdaq) with "indexes" - a list of stocks that is often the basis for index funds.

The Nasdaq 100 is not the same as Nasdaq. A company can be in many indexes but only one listing. There may have been competition for the listing but there is not competition between indexes for inclusion.

The implication is that Nasdaq (company) changed the rules for the Nasdaq 100 (index) in order to get the listing on Nasdaq (stock exchange).

Many companies are listed in multiple exchanges. Unilever, Shell, AstraZeneca, BP, and many more.

There was never a competition. It was explicitly designed to get a better "deal" where they wanted to open it.