Hello,
What @Neieus said is basically correct - for gaming your main concerns would be CPU, RAM, Graphics Card, but a hard drive can cause stuttering in some cases. For example, many games don't load everything at the start of the level, they load as they go as well. In such case an unsuitable HDD could cause stuttering. Also – if you use in-game recording software for example – it can cause the FPS rate to drop significantly due to slower write speeds.
The WD Green is designed for large capacity secondary storage, cool and quiet running. You will be able to run games, but keep in mind that there are (much – to be removed) better options for gaming, such as WD Black.
Hope I was helpful, Citizen_WD