Technically speaking, if they're a corporation then they have shares but they're just privately held.
So, depending on how they structured the purchase and sale of interest in the company, then if it was a straight forward purchase of interest then they either issued new shares and diluted the existing shares, or the parties involved sold some portion of their shares to the new investor(s).
It's hard to say which option they followed or whether they followed a combination of both.
If they sell existing shares then they pocket cash but they all get hit with capital gains. If they issue new shares then it's treated as a capital injection, but the existing shareholders don't receive any proceeds from the sale (no cash to pocket).
There are other options though it would create other complexities in the transaction. I suppose they could have done a share swap between Zuffa and the investing corporation, or even a share swap between the individual shareholders and the investing corporation.
Anyway, I'll stop there. Long story short there were shares.