What reasoning lead you to treat this apporach as an anxiety booster? Do you refer to using productivity apps in general?
Personally it was the opposite to me - various games increased my clarity, focus and the feeling of empowerment.
Though I have to say that gamifying life is about "creating a game" - game can be too difficult (lead to anxiety) or too easy (lead to boredoom) or the right one. Just like "normal" game for entertainment.
I created subreddit to gather people that gamify their life using "gamist approach" - approach where you are playing a game with your life by having a complex game/system (in spreadsheet, Notion, apps like Habitica etc.) and it gamifies your whole life rather than small part of it.
This approach is a niche of a niche and we want to create a small community to slowly spread this idea. If you did something like that - please join and post how you gamified your life.