Descriptively speaking, Ted's answer is basically correct, insofar as it accurately captures the kind of thinking that leads a lot of people to consider the term "Chinese virus" offensive. However, normatively speaking, the kinds of arguments Ted is putting forward aren't as strong as you might think.
It's always good to keep in mind that there's a variety of human biases constantly at work in politics. For example, the more punitive and controlling people within one's own political affiliation are often seen as unsung heroes of a worthy cause, while punitive and controlling people on the other side of politics are often viewed as jerks that need to be shut down and controlled.
I'm oversimplifying, of course.
With that said, notice that when you really look at it, Ted is basically advocating pre-emptive (before the deed) and vicarious (inflicted on a different person) punishment. In more detail, the idea is to control the way person A talks now (via e.g. social punishment) in order to prevent person B from doing something immoral later. Needless to say, this is not a good way of doing morality.
However, in the defence of people who consider this an offensive term, there is in fact a very good reason to avoid calling it the "Chinese virus".
In particular, a good way to use language in connection with controversial or emotive issues is to pick neutral words that don't presuppose your conclusion, and then, using those neutral words, build an argument in favour of your conclusion using evidence and reason.
In other words, you shouldn't choose words that presuppose your conclusion, because it's a way of evading the burden of responsibility for justifying your point-of-view.
A similar point can be made against the use of vague terms that are never defined; they might be effective at preaching to the converted, but they undermine your ability to contribute to the broader social dialogue in meaningful and positive ways.
In a nutshell then, the real problem with the phrase "Chinese virus" is that it's vague and emotive.
For example, in some ways, it really is Chinese (if we're talking about origins), for example. In other ways, it's really not (if we're talking about the relevant actual DNA sequence, for example.) And, furthermore, including "Chinese" in the name is obviously an attempt to put blame on a particular group of people. They may or may not deserve this blame, but you shouldn't choose a term that presupposes this conclusion
I therefore think it's clear that the phrase "Chinese virus" deserves criticism. And sure, the media has bad reasons for criticising it; yet it deserves criticism nonetheless.