Does it mean that whoever achieves the score 121 will be offered .......
I think we're all very uneasy about the tenses you're using, mariare.
What it means is "whoever achieved the score 121 in that particular year
was offered a place" (because the number of qualified applicants did not exceed the number of places available). Places cannot be left unfilled if there are qualified applicants (no matter where they live).
As Marylou & Guest55 have pointed out, what happens in other years depends on the numbers. If there are more children scoring 121+ than places available, it follows that not all of them can be offered a place.