Is this correct: "一个游戏有四个季度" I wanted to find out how to say a sports game has four quarters and the translation I received from Google was: "一个游戏有四个季度"

Certain sports games are split into 4 quarters rather than 2 halves and I want to express this, but I was interested in seeing "季度" used to mean quarter.

When I check Wiktionary there is no entry for 季度 but 季 says it is used to mean a quarter of a year or season.

Can 季度 also be used for other things that come in quarters?
No. 

A quarter in a sports game is usually translated as 节. For example, fourth quarter is 第四节. The first and second quarters are collectively referred to as 上半场 and similarly, the third and fourth quarters are referred to as 下半场. A sports season is usually translated as 赛季．

季度, when tranlated into English, only refers to a quarter of a year, as you have noted.