there are ways to structure businesses so that what you own is not a portion of the business itself [...] but only entitle you to a share of the profits or losses of the business. This is certainly how the dice sites are structured. You don't own any part of the site, just the profit/loss.
Your return as a dice site "investor" isn't based on the site's profit. It completely ignores all the site's expenses. The "investor" is just a counterparty to the "players". You can see them as another type of gambler.
Any profit the site makes can only be calculated after taking off expenses (hosting costs, advertising, staff, etc.) and isn't at all what the "investors" get a share of.
This is true, but this is analogous (but not identical) to a dual-class structure. The "owners" of the site have expenses related to their ownership of the business itself, while the non-voting class interests aren't tied to that portion of the business, just the gambling side where the profits or losses are on betting. In reality, I can't think of a situation where a business would structure things in such a way, as it's disadvantageous for the owners of the business. However, that doesn't change the facts the most important facts of the situation, which revolve around profit-sharing. It's just that you calculate the profits you're paying out differently.
In practice, you're paying for part of the business's expenses out of your own pocket (how kind!) and not considering "business profit" and "site profit" to be the same, but it doesn't change the fact that you're offering a portion of profits (a "profit-sharing agreement" as the SEC would call it). It's just you've structured your book-keeping in a way so as to be more advantageous to investors than it needed to be. Although, I might offer that your 10% claim on investor profits pretty-much makes this line of thinking moot. In any event, non-traditional bookkeeping doesn't excuse you from the definition of security (this would be an easy out, wouldn't it?).