Without Mugabe Zimbabwe would be a hell of a lot better off.
The POD is interesting because it means he dies before the Lancaster House Agreement is implemented, but after the Internal Settlement. It is easy to imagine the 1980 election might go a lot smoother possibly without as much voter intimidation. It is hard to see ZANU doing better without him, as they captured enough votes to secure an absolute majority in OTL. Edgar Tekere likely replaces Mugabe and in OTL he was fairly popular but, in my opinion, mainly because he was an alternative to Mugabe in the late 80s.
So with Mugabe dead in 1979, the 1980 election will go quite differently. Mugabe's (now Tekere's) ZANU will likely still be the single biggest winner at the elections but falls short of an absolute majority. I would hope that Bishop Muzorewa's UANC would pick up the extra seats at Zanu's expense and we might even see Sithole's breakaway ZANU-NDONGA Party pick up one or two seats as well. Nkomo's ZAPU is unlikely to pick up anymore seats since he captured all of the Matabeland anyway and his vote naturally peaked. Smith's Rhodesian Front will capture all the white seats, as in OTL.
The end result will mean that the party that forms Government will need to enter into a Coalition or Power-Sharing Arrangement. While it's tempting to propose all the other parties would band together to shut ZANU out, Tekere is a different man to Mugabe and there would probably be some attempt to negotiate with him.
One would hope this would lead to a far more prosperous and stable period for Zimbabwe, particularly since the politics will be dictated by compromise and moderation. That is, if the Governing party wishes to act within the law. A Gukurahundi event cannot be totally ruled out even without Mugabe at the helm, but ZANU's ability to carry this out will be much more limited compared to OTL. It certainly won't be from a position of absolute dominance.
I also expect that under this arrangement the Westminster system would remain in place and the Presidency Mugabe brought in later on wouldn't be adopted. This scenario might also allow for the continuation of a number of guaranteed white seats, at least for the purpose of retaining business confidence and international investment (even if the number of seats is scaled back to a symbolic number).