Can the service itself be profitable but the company not be? I mean how do we define profitable?

Presumably the employees are working below-market in exchange for equity, so the company is not really profitable yet - it's sort of "ramen profitable" in that it's profitable if you don't count the full rate of the workers' time.

If the service is provided by employees who are compensated with equity, why would you not count that in profitability numbers?

Because that's literally one of the reasons to use equity based compensation.

The figures above are with GAAP standards but as a private company do they actually have to use that?

It certainly helps if you plan on going public at any point in the future.

Taxation, I guess?

There's a lot of ways to measure "profitable".

Judging from their current numbers the service is profitable on a per user basis, less marketing expenses.

This is a pretty reasonable way to look at it. Being cashflow positive means you can turn up marketing to grow and turn it down if needed.