Ruling on eating game caught by one who does not pray
Question

                I have a relative who is a hunter, but he is a person who does not pray. Is it permissible for me to eat the game that he shoots? Please note that he may not mention the name of Allah before shooting.
Praise be to Allah.In the answer to question no. 2182 we discussed the ruling on the one who does not pray, and stated that the one who does not pray is a kaafir. 
You have to try hard to advise your relative and remind him of the seriousness of not praying and the gravity of that offence. For more information please see the answer to question no. 47425, which discusses the way to call one who does not pray. If he turns away after establishing proof against him, then you should leave him and shun him, so that he will not have any influence on you. 
See the answer to question no. 4420
Secondly: 
For game to be halaal, it is stipulated that the hunter should be one whose slaughtered meat is permissible, in the sense that he is a Muslim or a Jew or a Christian. It is not permissible to eat meat hunted by a mushrik, Magian (Zoroastrian), atheist communist, apostate, and the like. 
Al-Bahooti (may Allah have mercy on him) said in Kashshaaf al-Qinaa‘ (6/218): With regard to hunting, it is stipulated that the hunter should be one of those whose slaughtered meat is permissible, because the Prophet (blessings and peace of Allah be upon him) said: “Being caught by the (hunting) dog is (equivalent to) slaughter (in the prescribed manner).” (Agreed upon).
Based on that, the hunter is equivalent to the slaughterer, so it is stipulated that he should be qualified. End quote. 
Based on that, it is not permissible for you to eat game caught by your relative, because the one who does not pray is a kaafir and apostate, so it is not permissible to eat meat slaughtered by him or hunted by him. 
And Allah knows best.