"I did not run recently."
Translation:Níor rith mé le déanaí.
Yes. Because R doesn’t lenite (or eclipse), rith mé could mean either “I run” or “I ran”. This might be a reason for the Caighdeán preferring synthetic first-person present tense conjugations — rith mé would be unambiguously past tense, since the present tense form in the Caighdeán is rithim. (Rithim is also the first-person singular imperative form, but context usually clarifies when such an imperative is being used.)
Abair is an irregular verb. The rule for irregular verbs is that irregular verbs are irregular - they don't have to follow the rules that apply to regular verbs.
The rule for the past tense is that you use níor as the negative particle. Some irregular verbs follow that rule, some don't (because they're irregular).