These are some great features! I expect Monzo will solve this for you but perhaps not quite in the way that you’ve described…
It looks like users won’t be able to create their own categories in the foreseeable future for this reason -
https://community.monzo.com/t/custom-categories-1/649/14
Having said that, the categories are due to be reviewed, once the current accounts launch. So if there are other categories, in addition to the one’s you’ve mentioned, please do point them out.
Obviously they need to be useful for most users so I expect a category like games is unlikely to be created. Having said that, you would be able to monitor your spend on games if you added a dedicated emoji to the notes of a transaction, each time you buy them. So perhaps that helps?
Monzo are going to enable you to set custom timesframes for your targets & it looks like we might get that feature 
The virtual savings pots feature might help with this too - if you could set aside any money that you’ve saved each month, in a dedicated ‘shopping’ pot?