I think those are good examples. I think part of the confusion is that most of those are typical responsibilities of e.g. senior level IC work, so "performance at your boss's level" looks more or less the same as "performance at your current IC level".
I'd say it's about doing things at the next level to show you're ready for that level. So for moving from a Sr to a Staff position might involve doing more mentoring of the team, showing that you are using your knowledge to improve the efficiency of both your team and other teams, etc.
Which is good advice! Do your job well!