Not really. There are a variety of ways to participate in Private Equity...direct ownership, partnership, non-voting shares, etc. However, the model Fig seems to be using is one in which money is pooled from a variety of investors by PE fund managers, put into a time limited fund, and then invested by an investment fund manager (usually the same people who put the fund together in the first place).
This fund has a ramping up period (where funds are used to acquire investments), and a winding down phase (where investments are sold off for what the fund hopes is a profit). In Fig, an investor has a return schedule where he's paid up to certain $ amounts and then a percentage of revenues thereafter. This is a bit different than owning an interest in a company, as your involvement is on a project to project basis.
Here's an example of this PE model: