That is also accepted. This course tries to teach the various ways of saying 'want' in Norwegian, and while this might sound somewhat formal, it is still acceptable to say it. 'vil ha' would, as you say, be more common.
Why isn't it, " Jeg ønsker meg iskrem I stedet!"? I have seen the 'meg' in other sentences using ønsker. Is the 'meg' optional? I believe I've been counted wrong when I forgot to put the 'meg' into the sentence... Thanks for the advice!