Although if I have to link some Priest songs with Richie that have this kind of vibe, maybe ''Flame Thrower'' and the 2014 bonus song ''Bring It On''.
He said in the interview above that this project is not a full-on metal band, some of the songs are more classic rock and some of the bluesy elements (which Rob liked) could be on an early Priest album. That's normal, Priest's discography is quite diverse.
What's great about Richie as a songwriter is that he writes very melodic catchy songs and great riffs, and I think Priest's style changed a bit with him. Some of the songs have Maiden vibes to them. Speaking of which, I'm really curious what song Richie would write with Steve, Bruce or Adrian.