You could argue it is still being used for the same purpose - assessment of suitability for employment with a specific company/group. I think the period for data retention is loosely defined - as long as it is relevant to the purpose, which it would be if the assessment has been proven to have test-retest validity (most do) and if the company can show candidates reapply within two years (case in point).
You can always ask if they'll let you retake the test for the reasons you state (were stressed when you previously took it, etc.). You may have been automatically knocked-out based on whatever score was already stored on the system. A human may be more generous, although if they're confident in the test's validity they may not see any point in paying for another assessment.