Mullich's began working in video game industry in 1978 when his COBOL professor at California State University, Northridge hired him to work as a clerk and programmer at Rainbow Computing, an early computer store in the Los Angeles area. Sherwin Steffin, who was a frequent customer at the store, recruited Mullich to develop games for his new start-up game publishing company, Edu-Ware Services. Upon graduating in 1980 with a degree in computer science, Mullich joined Edu-Ware as a full-time employee, and as his first assignment created the adventure game The Prisoner.
Mullich designed most of Edu-Ware's adventure games and role-playing video games, and programmed the company's EWS3 graphics engine and many of its educational programs. Edu-Ware's Space game series were accused of violating the copyrights of Game Designers' Workshop's tabletop game Traveller. Mullich redesigned the games and started a new series called Empire. Windfall: The Oil Crisis Game was an early simulation video game. He eventually left Edu-Ware for Electric Transit.
In 1987, Mullich joined Walt Disney Computer Software, where he produced video games based upon Disney characters, films, and television shows with external developers and licensees. He left due to internal politics from upper management. In 1991, he joined developer Interactive Support Group to create driving and action games for fifth-generation console systems CD-i and 3DO. Mullich next became development director at game publisher Cyberdreams, where he became involved with I Have No Mouth, and I Must Scream as soon as he heard about its development.
While participating in a game design panel at the Computer Game Developer's Conference, Mullich met Jon Van Caneghem, founder of game developer New World Computing. Van Caneghem hired Mullich in 1997 to lead the Heroes of Might and Magic III development team. Mullich led the team through Heroes of Might and Magic IV. The hero Sir Mullich in Heroes of Might and Magic III: Armageddon's Blade is named after him. With the financial demise of parent company The 3DO Company, Mullich left New World for software publisher Activision, where he worked on Vampire: The Masquerade – Bloodlines, a role-playing game based upon the Source engine. When his contract with Activision concluded, Mullich was hired by fellow Cyberdreams alumni Jamie Ottilie to be the development director of his mobile game publishing start-up, Abandon Mobile.