If you want to play some games, then play them.
The idea that Christians are forbidden from engaging in innocuous activities like watching movies, listening to music, playing video games, or growing a flower garden is an incredibly bizarre idea to me.
Some things are moral issues, namely how we treat other people. But much in life isn't a moral issue--what food to eat, what clothes to wear, what brand of shampoo to use, movies, television, music, other forms of entertainment, playing sports, and various other mundane activities.
Throughout the New Testament we find St. Paul talking about the importance of Christian liberty of conscience, and to allow differences between Christians concerning matters of conscience. The Apostle shows very little tolerance for the sorts of moralistic busybodies going around saying "don't handle, don't taste, don't touch" (Colossians 2:20-23). Instead the Apostle consistently teaches that when it comes to things like what we eat or drink, or other such matters that we are to follow our conscience and not let others judge us and not to judge others,
"One person believes he may eat anything, while the weak person eats only vegetables. Let not the one who eats despise the one who abstains, and let not the one who abstains pass judgment on the one who eats, for God has welcomed him." (Romans 14:2-3)
The idea of weakness of faith here may sound weird, but the Apostle has in mind the idea that people who may not know better--that they are free to eat as they want--may suffer from guilt of conscience. The Apostle instructs neither belittling nor judgment, but a loving acceptance of one another in Christ.
This means that the only person who can decide whether or not it's okay for you to play video games is you. As you are a new convert, I would also hope that you are part of a healthy, loving, and uplifting church community and, therefore, can receive good pastoral counseling and guidance as you are beginning your road toward Christian living. A good pastor would happily help you through these things, letting you know that being a Christian doesn't mean there is suddenly some complex rule book to follow, but that being a Christian means sharing in the life of the Church.
Does your current church provide some kind of religious formation/education for new converts? In many mainstream churches this is usually a kind of Sunday School program that will help lead you toward eventually receiving Baptism, such explaining the basics of the Christian religion, helping answer questions that you have, etc. It's also usually pretty open, meaning there isn't necessarily any obligation for you to join if you don't want to. Any church worth its salt will have those options available, with transparency, honesty, and without coercion to help you grow and help you get your footing.
-CryptoLutheran