In the name of Allah the Most Gracious the Most Merciful
The answer to your question is as follows:
To divide qurbani meat into three portion, as mentioned in the question, is mustahab (recommended), and not necessary. The person can keep more than two third to consume or to give to his relatives if he needs. You stated that ‘those who didn’t do qurbani’ denotes that there must be some faqeers (who were not able to do qurani). ‘Faqeer’ doesn’t mean that they are faqeer in term, but needy persons also come in category of faqeer. Though the faqeer in term is preferable.
And Allah Knows Best
Darul Uloom Waqf Deoband