Absolutely the hanger should be checked. I personally would start with replacing the cable and housing and see if that resolves the issue. Looking at how that cable is routed especially where it enters the derailleur I'd bet that's more of an issue than the hanger. It looks like the ferrule is being pulled out of the derailleur the ferrule should be going straight into the derailleur with no tension on it.
that housing is WAY too short.
1. Replace the housing
2. Start again with the adjusting screws
if that doesn't fix it, check the hanger alignment
...then start again with the adjusting screws
If it's a new bike, whoever sold you the bike should fix it at their expense. If you did it yourself, it's a good lesson.
Also, use Shimano SP41 housing - it's the best
Go well
