"Sports Illustrated" had it right: for Magic and Bulls, this year was not just about the championship, but a battle for survival.
If the Magic couldn't win the championship, Rich DeVos definitely wouldn't offer Shaq the contract he wanted. After all, he isn't Paul Allen or James Dolan.
He had indeed made a promise to Shaq, but the promise was contingent upon winning the championship.
The same issue was present with the Bulls too, not that Jordan would want to leave if he lost, but if they couldn't win the championship, the Bulls might not offer him a contract commensurate with his value.
Considering Jordan and the Bulls management hadn't been on good terms, he had no chance of lowering his price to stay with the team.
Furthermore, it wasn't just Jordan who was testing the free agency market for the first time; if the team couldn't win the championship, both coach Phil Jackson and Dennis Rodman's futures with the team were in huge doubt.