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I get that, if code is open source then others are free to build whatever they want with it. My questions are more geared specifically towards the website steemit.com. Are there no rights to a website someone builds on a blockchain?

No, there is no rights to tell people they can't build on a blockchain. The system is trustless. Did you notice smoke.io doesn't list account USD values? This is for a reason. The code isn't even the same, steemit inc can learn from this code. Innovate or die.