Not necessarily. The sentence you've quoted is perfectly correct as well.
Here are some sentences I've dug up where impact isn't followed by on:
Both events negatively impacted her life.
The book discusses the impact of Christian thinking on western society.
from Cambridge Dictionary
...the potential for women to impact the political process.
from Collins Dictionary
As far as I can see, your definition of impact (verb) can be used in four different ways: (from Collins Dictionary):
VERB + on/upon
Such schemes mean little unless they impact on people.
VERB on/upon noun
The reduction in the number of days that Parliament sat would impact on the quality of its work.
...the potential for women to impact the political process. (mentioned
Trading is being increasingly impacted by the current recession.
Hope I've helped!