The WTO primarily operates on a consensus based system for decisions making.
"The WTO is ‘member-driven’, with decisions taken by consensus among all member governments."
"The WTO is run by its member governments. All major decisions are made by the membership as a whole, either by ministers (who meet at least once every two years) or by their ambassadors or delegates (who meet regularly in Geneva). Decisions are normally taken by consensus."
"The WTO continues GATT’s tradition of making decisions not by voting but by consensus. This allows all members to ensure their interests are properly considered even though, on occasion, they may decide to join a consensus in the overall interests of the multilateral trading system."
Finally, see the "Understanding on Rules and Procedures Governing the Settlement of Disputes" from the WTO which sets out the dispute resolution framework and WTO rules:
"Article 2 Administration
4. Where the rules and procedures of this Understanding provide for the DSB to take a decision, it shall do so by consensus."*
*"DSB shall be deemed to have decided by consensus on a matter submitted for its consideration, if no Member, present at the meeting of the DSB when the decision is taken, formally objects to the proposed decision."
Article 17 Appellate Review
2. The DSB shall appoint persons to serve on the Appellate Body for a four-year term, and each person may be reappointed once. However, the terms of three of the seven persons appointed immediately after the entry into force of the WTO Agreement shall expire at the end of two years, to be determined by lot. Vacancies shall be filled as they arise. A person appointed to replace a person whose term of office has not expired shall hold office for the remainder of the predecessor's term.
So the provisions vesting Appellate Body appointments in the DSB (Dispute Resolution Body) and the DSB operating by consensus, meaning if any one member "formally objects" then the decision, or in this case appointment is blocked.