You can probably get away with doing this action, because you will be making this shirt for only your personal use. However, I do not recommend you do this or engage a third party to print this shirt for you, because it is very likely either a trademark or a copyright infringement.
You may not have to worry about trademark infringement issues in the symbol unless the symbol is so iconic that it is representative of the video game as a whole and perhaps even as the source of some video game (e.g., the distinctive mushrooms from Super Mario Bros. being used on a product to indicate that the product's source is Nintendo ). Nevertheless, there must be some level of secondary meaning or source indicator associated with this symbol if you are wanting to include the symbol on a shirt for people to see.
Copyright will exist in the original, creative design elements in the symbol and these original designs are likely owned by the video game company or other third-party source code provider. Your replication of this symbol will infringe the copyright owner's exclusive right of reproduction and adaptation for derivative works. Copyright will also exist in the image of the symbol that you pull from the video game company's website.
Perhaps you could see if the video game company has released a patch of this symbol that can be sewn into or incorporated into your custom shirt.
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Q: "The shirt would just be for me to wear I wouldn't sell it nor replicate it. Can I do this?"
R: Yes. Even assuming the "symbol" is copyrightable and serves as a trademark, making one shirt for your own personal use that displays that symbol and which will neither be sold nor given away is not conduct of any concern to the law. And, no, making one copy of a copyrightable work that will see most of its life in a dresser drawer is not even "technically" copyright infringement because it's de minimus.
The above response is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
Can you? Yes, Should you? maybe.
In principle you should not use somebody else's property, such as trademarks and copyright. having said that, your propose use appears to be de minimis, meaning let him go, and most likely will not be prosecuted.
Of course if you like to sell it to your friends, then you are on your own and the maybe turns to a stern NO.
USPTO Registered Patent Attorney, Master of Intellectual Property law, MBA I am neither your attorney, nor my answers or comments in AVVO.com create an attorney-client relationship with you. You may accept or disregard my free advice in AVVO.com at your own risk. I am a Patent Attorney, admitted to the USPTO and to the Florida Bar.
As long as you're doing it for your personal use, not selling it or mass producing it, you should be fine.
I focus my practice on (video) gaming industry, casino gambling, and complex internet law issues, electronic free speech, entertainment law, copyright and trademark law, and computer fraud. I primarily represent game developers and founders of emergent internet technologies. The author is a Maryland attorney; however no answer given on Avvo is intended as legal advice or intended to create an attorney-client relationship.