He works in a video game store and is asking about his income

If the work is permissible, and there is no sin involved, then the wages that you receive are also permissible. This is the basic principle with regard to work and employment. 

Based on this, if your work in the games arcade does not involve doing anything wrong, or approving of or helping others to do wrong, such as staying away from prayer in congregation, listening to music, playing games that involve gambling, or other such evils, then is nothing wrong with you continuing in that, and the wages that you earn are halaal. 

Prayer in congregation in the mosque is obligatory according to the more correct of the two scholarly opinions. See questions no. 40113 and 8918. 

Listening to music is haraam. See question no. 5000 and 20406. 

The fact that it is obligatory to denounce evil is indicated in a great deal of evidence, such as the words of the Prophet (peace and blessings of Allaah be upon him): “Whoever among you sees an evil act, let him change it with his hand (by taking action); if he cannot, then with his tongue (by speaking out); and if he cannot, then with his heart (by at least hating it and regarding it as evil) – but that is the weakest of faith.” Narrated by Muslim, 49. 

The fact that it is haraam to help others commit sin is indicated by the verses in which Allaah says (interpretation of the meaning): 

“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah. Verily, Allaah is Severe in punishment”

[al-Maa’idah 5:2] 

“And it has already been revealed to you in the Book (this Qur’aan) that when you hear the Verses of Allaah being denied and mocked at, then sit not with them, until they engage in a talk other than that; (but if you stayed with them) certainly in that case you would be like them. Surely, Allaah will collect the hypocrites and disbelievers all together in Hell”

[al-Nisa’ 4:140]

 al-Qurtubi (may Allaah have mercy on him) said: The phrase “then sit not with them, until they engage in a talk other than that” means: talk other than kufr. “(but if you stayed with them) certainly in that case you would be like them”. This indicates that it is obligatory to avoid people of sin if they commit evil openly, because whoever does not avoid them is approving of what they are doing, and approving of kufr is itself kufr. Allaah says (interpretation of the meaning): “(but if you stayed with them) certainly in that case you would be like them”, so everyone who sits in a sinful gathering and does not denounce them shares the burden of sin equally with them. 

They should be denounced if they speak of sin and do it. If a person is unable to denounce them then he should leave so that he will not be among the people mentioned in this verse. End quote. 

We ask Allaah to help you to obey Him and to avoid sin, and to bless you with halaal provision. 

And Allaah knows best.