Now let's get down to business...
Is MatPat in the wrong?: No, MatPat was not in the wrong for giving the pope Undertale. Undertale was a rather strong message about the value of pacifism (albiet the Undertale fandom inflates the message to point of being Anvilicious ) and how it fits within how the pope declared this as a year for mercy for the catholic church. But is MatPat completely in the right? Again, no. This is because the video is not very humble about this, however I'll go more in depth with the video shortly. What doesn't help this is how many people are against the Undertale fandom itself, who complained about the fact Undertale was chosen as the gift, thus adding to the heat.
Is the video in the wrong?: Yes, starting with the clickbait thumbnail and the cold opening at the beginning (only crack fic writers should be the only ones to say that Undyne is Pope Francis or vice versa). But MatPat bragged about it and used recent events as leverage (this would be fine had the video came out before the whole controversy revolving around how nobody does anything to stop mass shootings from occurring) and said how gamers are pigeonholed outside of the gaming community. But is the video the worst, no, Drama Alert takes that cake. Is this at least, the most cringey Game Theory episode? nope, that goes the whole episode about how Sans is really Ness from Earthbound, and by extension, claiming its canon.
In conclusion, I'm fine with MatPat giving the pope Undertale, its just that the video hits people harder than a bullet train smashing into a car made of popiscle sticks and glass.
TL:DR: MatPat gives pope Undertale, good. MatPat made video of it, bad.