First off, check your contract (assuming you have one). It should list:
- Required notice before leaving
- Any other conditions involving signing bonuses, vacation days, etc.
This will give you the bare minimum for you to quit without being in violation of your contract. This will not make leaving tactful, but it will at least make it contractual. Which is a good start.
The biggest issues for an employer when someone leaves are:
- Handing over work responsibilities
- Finding a replacement
- Training a replacement
Ethically you want to make those three steps as smooth as possible.
I don't know your position or importance to the company, but you've only been there for 6 weeks. I doubt you are a cornerstone of their entire business strategy. Also, only being there for 6 weeks means that you probably don't have that many work responsibilities that weren't recently handed over from someone else.
What I would suggest is that you share your notice (in agreement with your Contractual Responsibilities) above, and explain that while you will be leaving, you want to make sure to help make the transition as smooth as possible for the company. Depending on how difficult it is for the company to find a replacement, or how hard it is to transfer your duties, you may want to offer to stay on beyond your contractual responsibilities.
Ideally you could find a way to stop working full time at the conclusion of the notice period, but (if required) help with training/handing over of duties part time giving you time to work on your game while still being able to support the company (in a more limited role). Depending on the flexibility of the HR, the nature of the salary/benefits, and the size of the company, this may not be possible.
The sooner you tell them the better. If you were hired only 6 weeks ago, other candidates may still be hunting for a job and could be hired without having to start the process over (this is much cheaper/easier for the company). The longer you wait, the longer it will take to find someone to do your job. The more the company feels it depends on you (and the closer the deadline of your leaving looms), the less cordial the parting will be.
Good luck with the game, and make sure you repay any coworkers you lost bets to before you leave (or return any rounds of drinks that may have been bought for you when you joined).