In this context, I would take any list of rules that dictates buying securities to be an index.
For example, a fund buys an equal number of shares of every publicly listed company.
Or a fund buys securities that trade with a ticker symbol starting with the letter C.
Based on that definition, one could refer to a Cathie Wood index fund to be composed of whatever she decides to buy and a bagacrap index fund to be composed of whatever bagacrap chooses to buy.