While I agree that it boils down to semantics, I actually disagree on the scientific use of the term in the comments. In astronomy, we know there's a difference between gas and plasma, but we almost always use the term "gas" when talking about what's in stars. E.g. "the fraction of gas locked up in stars" (as opposed to in the interstellar medium). We also talk about the metallicity of gas, meaning both gas and plasma. I think we only use the term plasma when specifically discussing properties that are unique to plasma, like being "frozen" in magnetic fields. And googling ["ionized gas" -plasma] (the '-plasma' is to get rid of articles explaining what plasma is) returns 243,000 hits, of which by far the most seem to be scientific papers and websites.
So I think the answer is: "No, stars aren't made of gas, they're made of plasma, but go ahead and call it gas, you won't offend any astronomer."
However, I agree with Rob Jeffries that we don't like when you call it burning gas. It's nuclear power! It's a million$^\dagger$ times more powerful than fire!
$^\dagger$Why "a million"? Because nuclear reactions are measured in MeV, while chemical reactions are measured in eV.