Starship is specifically designed to fly to and land on Mars:
That said, they could update the page, it's 2022 already and promising great things in the future year of 2020 is not a good look.
And while I do not want to besmirch SpaceX engineers working on it, the website is not a statement from them, it's a statement from PR machinery. Which holds similar weight as "FSD is next year" being told for 7 years by Tesla PR.
If they manage it, congrats. If not, I still reserve the right to laugh at the PR machine (not at the engineers, they have a hard problem to solve that isn't helped by overpromising PR).
I do not have high hopes in that design.