There are organisms with anaerobic metabolism that tolerate oxygen: aerotolerant anaerobes. "Anaerobic" refers to the metabolic system. You cannot be sure of oxygen tolerance based solely on metabolic system.
Factors influencing the tolerance of anaerobic bacteria to oxygen
Here is why this is a facultative anaerobe.
This organism does not gain weight when denied air. One concludes its metabolism is less efficient.
> Curiously, the consumption of sugar increases as air is removed from the organismʹs enviroment
Anaerobic metabolism uses sugar less efficiently than aerobic metabolism in organisms that can use both methods. This means oxidative metabolism is the preferred method.
So: this is a facultative anaerobe because it can get by using anaerobic metabolism, but two pieces of information show that for the organism, anaerobic mode is less efficient than aerobic metabolism. Brewers yeast is such an organism.