Best to avoid as the term can be confusing. It is not a synonym for the Olympics. It is a period of four years beginning on Jan. 1 of the Olympic year. Olympiads are numbered consecutively in Roman numerals from the 1896 Athens Games. These are the Games of the XXXI Olympiad, which began Jan. 1, 2016.
Here are some other tips from the topical style guide:
— Rio is OK on first reference, "provided that you use the full name, Rio de Janeiro, somewhere in the story, preferably high up. Rio is also acceptable in headlines. This is an exception to our usual guidance on city names, acknowledging the prevalence of the shorthand Rio in common parlance. The dateline should always be the full name of the city. Examples: Olympics in Rio de Janeiro, Rio de Janeiro Olympics, Rio de Janeiro Games, Rio Olympics, Rio Games."
Adjective (without s) and always capitalized: Olympic gold medal, Olympic organizers, Olympic host city, Olympic flame, etc.
Noun. Always capitalized.
— Games, games
Capitalized when attached to the host city or year: the Rio de Janeiro Games and the 2016 Games. When standing alone, spell games lowercase: The games open Aug. 5.
There's a lot more guidance, which you can explore here, including a pronunciation guide. For instance, Ipanema – "ee-pah-NAY-mah."