You can do - as mentioned, we only actively monitor the games tag, so any game related questions that pop up under a different tag will be missed by our community. The best way to handle this would be to synonimise all gaming related tags to games. From what I can see, this has already been done. (both gaming and game are synonyms of games)
If there are any other additional tags that you would be considering creating synonyms to games you should probably list them before a community consensus is built and any action is taken.
The exception is the game-recommendation tag - any questions with this tag will be ignored by our community because recommendations are strictly off topic and are closed within minutes of being asked.