The four-quadrant matrix I am familiar with is:

                      Urgent  Not-Urgent
    Important             Q1          Q2
    Not-Important         Q3          Q4

- Q1: Do it now

- Q2: Do it the next time you can

- Q3: Do it now or don't do it at all

- Q4: Don't do it at all

Compare this to the modified matrix:

                    One-Time   Repeating
    Important            MQ1         MQ2
    Not-Important        MQ3         MQ4

If I understood your post, the translation is:

- MQ1: Do it yourself

- MQ2: Delegate

- MQ3: Don't do it at all

- MQ4: Delegate but maybe not done at all

It is interesting that Q1->MQ1 and Q2->MQ2 quite straightforwardly, but (Q3, Q4) -> (MQ4, MQ3) seem to be swapped.