"he waits" and "he is waiting" is the same thing... both work for the translation.
It is and is not. One strongly suggests it is happening right at this moment. And so does the word čeká. To suggest otherwise and make it a regular repetitive activity you would need to squeeze in something like "always waits" "vždy čeká" .
It is not possible to tell wether he or she is waiting so why is one of it wrong?
Both 'he' and 'she' are accepted.