Horizon League does not sponsor gymnastics or wrestling. So they can join a conference as an affiliate.
Likely NIU will stay with MAC for gymnastics and wrestling as affiliates, since MAC will continue to sponsor those sports championships.
It is not uncommon for Universities to be part of a main conference, but have multiple sports in affiliate conferences. Especially for the Olympic sports in which not as many conferences will sponsor a championship (because you need 4 teams in a conference to sponsor a conference championships).
Denver is a prime example.
University of Denver offers many sports.
Their primary conference is The Summit League.
The Pioneers compete in The Summit League in men's and women's basketball, golf, soccer, swimming and diving, and tennis. Additionally, women's volleyball.
Denver has several athletic teams that do not have a Summit League championships.
So they are affiliates in conferences that sponsor a championships.
Women's gymnastics is part of the Big 12.
Lacrosse (M and W) are both part of the Big East.
Skiing is in the Rocky Mountain Intercollegiate Ski Conference (RMISC).
Hockey is in the National Collegiate Hockey Conference.
If you look at Men's Gymnastics, MPSF conference is made up of:
Oklahoma (SEC), Stanford (ACC), Cal (ACC), Air Force (Mountain West).
In Women's Gymnastics, MPSF is UC Davis (Big Sky-soon to be Mountain West), Sacramento State (Big Sky soon to be Big West), Alaska-A. (Great Northwest Athletic Conference), Southern Utah (Western Athletic Conference soon to be Big Sky).
I think it's a great thing to be able to be an affiliate team should your school choose to sponsor a team, but there are not enough conference teams to sponsor a conference championship.