Almost all your points are about immigration. Yes, they have certainly moved to the right on immigration. Even the centre-left social democrates have moved right in this regard. But that still doesn't make the conservatives a right-wing party.
Compared to the past they have also moved left on other topics: e.g. by not touching pensions.
"restricts skilled immigration": Funny, since they have also been criticized for allowing more immigration. Ironically from left-leaning people.
"reduce social support systems": Well, they mostly retargeted social support. All polls showed that a large majority of the people supported these changes. People thought the old system enforced the wrong incentives.
Also let's not forget that they reduced taxes on salaries specifically for working-class families substantially.
"lowers corporate tax rates": IIRC they have only lowered one tax slightly for a single sector (tourism) so far. Hardly anything dramatic.
Still, all these points are not too surprising for conservatives in general. If this is enough for you to call them right-wing, that's certainly fine for me.
Just to add: I've talked to people that directly called the Austrian conservatives an extreme right party ;) I know you didn't go as far, but they were also pretty serious about that. Maybe we can agree that at least "extrem right" is ridiculous. I personally don't get where this overly-dramatic phrasing comes from. Are some people so upset that for once the chancellor is not a social-democrat?