I think it would absolutely be worth it. No school has a median LSAT above a 173 https://7sage.com/top-law-school-admissions/ and a 4.0 is over every school's 75th. Focusing on games sounds like a good strategy, especially for faster results!
Even after the median increase, a 171 is still a 75th percentile or better score for most schools. Get your apps perfect and have them submitted as early as possible. A retake would help but I'm not sure how much.
Depends on the school since different schools value GPA and LSAT differently, relatively speaking. However median LSAT and 75th GPA sounds like you'll have as good a shot as almost anyone.