Term for a humorously hypocritical last sentence at the end of a lecture

Consider punch line or punchline, defined as:

The final phrase or sentence of a joke or story, providing the humor or some other crucial element.

This definition explicitly allows that a punchline may appear at the end of something other than a joke, for example, a story.

A punchline might also appear at the end of a humorous notice warning Pokémon Go players about disrespectful behavior. The presence of a punchline does not necessarily mean the notice was written completely in jest.

The final sentence of the notice you link to certainly has the feel of a classic punchline. It's unexpected and humorous. Everything else in the passage misdirects readers from thinking the priest also plays the game. This material is called the set-up.

Punchline works well in your example:

At the end of a long notice about proper Pokémon Go behaviour, there was an unexpected punchline.

You might also say that there was a humorous twist, where twist means:

an unexpected development of events.

In your sentence:

At the end of a long notice about proper Pokémon Go behaviour, there was a humorous twist.

The "Kicker"

Something that provides a big kick or thrill.

The point of a joke; the fallacy in an argument; an item in a group that invalidates, negates, or makes worthless all the others.

"The kicker to this one is simple, but the background is…involved.…", NYTimes Magazine, Gilbert Milstein April 8, 1951 17/2

possibly tag line (or tagline)

dictionary.com

1. the last line of a play, story, speech, etc., used to clarify or dramatize a point.

Merriam Webster

1 : a final line (as in a play or joke); especially : one that serves to clarify a point or create a dramatic effect

American Heritage dictionary

2. An ending line, as in a play or joke, that makes a point.

I might use "zinger." As far as I know, it's another perhaps more colloquial form of "kicker," but I will edit this post shortly with some more info. I'm on my phone at the moment.