First of all, you need to admit your mistakes and realize that it's not right to snub your girlfriend because of playing games. Be honest about your apologies and don't make excuses or pass the buck.
Having open and honest communication with your girlfriend is the key to solving problems. Find out why she feels left out and how she wants you to improve. Through communication, you can find a mutually acceptable solution.
To make sure that something like this doesn't happen again, you need to have a plan in place. This plan should include reducing the amount of time you spend playing, increasing the amount of time you spend with your girlfriend, and making sure you're able to be there for her when you need it.
In addition to verbal apologies and promises, you also need to prove your care and love for your girlfriend with practical actions. For example, prepare her a delicious dinner, accompany her to the movies or go for a walk, or write a sweet letter for her.
Finally, it's important to give your girlfriend enough time to accept your apologies and changes. Don't rush things and give her some space and time to process her emotions. At the same time, you also need to be patient and not give up easily.
In conclusion, when you have snubbed your girlfriend because of playing games, it is very important to admit your mistakes, communicate, make plans, and take practical actions to prove that you care and love her. At the same time, give her enough time to accept your apologies and changes. Hopefully, these suggestions will help you coax your girlfriend back and make your relationship stronger and happier.