But the expression "meet up" has taken on the meaning of:
"A pre-planned gathering (for social interactions) of a large number of strangers with something in common"
Therefore, it is more specific than a general word "meet" -- which has all kinds of uses to describe all the ways in which people come into the presence of others.
Here's a link to Meetups.com - a web site that facilitates starting or locating meetups
Do something, Learn something, Share something, Change something - Meetup.com
That means that the use of "meet up" in your example is somewhat gratuitous. It's still a possible use, but I would edit it out and leave only "meet." The author liked the choice because of its more casual feeling, more impromptu, or friendlier, warmer .... I think it was used by the author to "soften" the "blind date" implications.
I think it might often be said:
"On Monday, I'm meeting my parents to go to a play, and on Tuesday I'm meeting up with a guy from my online dating service."
Student or Learner