The sentence in concern has too many adjectives and that might have confused you. Starting dancing this way could be vague and he invited everyone to join, that's even strange. But try to group those adjectives and the sentence might look better.
Okay, that’s [vaguely annoying] in an [over-enthusiatic motivational speaker] kind of way, but...
Let's not judge the event but what it means is the dancing and invitation both was done in a way some over-enthusiastic motivational speaker would do.
Not exact but this could be something like...
You dance in an MJ way.
means you dance the way MJ danced.
Said that, this is vaguely annoying. How? In a way some over-enthusiastic motivational speaker would speak.
Edit after OP's comment:
Here, vaguely means slightly. It was a bit strange and so slightly annoying that he was about to dance that way by inviting people.