When you reach this screen, you're done.
Bubble Safari is probably the worst offender in invite sending and game progression.
There was a report by Kotaku about the time it takes before either sending requests to friends or paying in Mafia Wars 2 to proceed in the game. Bubble Safari sets a new record for this, rolling out your first wall post within the first minute of gameplay (if you're not careful with unchecking the small 'share coins' box in the corner) and requiring you to invite more friends around 7 minutes in.
After so many people sent me requests to this game, I've decided to try it out, since it must be popular... or something. I was wrong about this.
Played through five levels of what is just Zynga's version of a bubble shooter (which are more like tutorial levels), and ended up with the above screen. An ordinary 'require friends to proceed' page, right? Not exactly.
Not only do you have to send requests to three different friends (and maybe more later on), but you have to send these requests to friends not already using the app, and they have to play the game and press the accept button from there. This, of course, is not guaranteed to occur unless you happen to control the accounts that you sent your requests to. (If they have a stance about multiple accounts, they're doing a very good job promoting them.)
Although you can skip this once using the premium cash given to you at the start of the game (which lets you go through around 10 more levels), you have to do the invite process at least five more times throughout the course of the game (total of 15+ new friends invited, provided another person didn't get to them first), and you can't grind premium cash by leveling up, completing missions, etc.
Seeing there's no way to really progress through the entire game, let alone 10% of it without bothering my 'actual' friends with requests in order to proceed, I promptly removed the app.