>They're not governments, they're companies.

You're right, it's important to note they are more powerful and exercise more control over the lives of their employees than many governments, though employees often have the same opportunity to leave their company as they do their government (none).

>It isn't, unless your definition of "personal rights" includes "things I personally want which are neither codified in, nor protected by, laws."

Yes that's literally exactly what personal rights always means. Legal rights are legal rights, personal rights are a conception of what the person who uses the term wants or believes rights to be.