It might be truly anti-competitive "ladder-up-behind-you" if all app devs were forced to sponsor client-side traffic. Think of taxi tokens- a fixed barrier to entry.
But even then, to be an anti-competitive barrier to entry it must also be high. The cost of a postage stamp on your government paperwork is a barrier to entry, but it is not anti-competitive.
To me, its similar to a supermarket only allowing already-popular brands to be on their shelves. From their POV I guess it makes sense, but if you're out there selling a new brand of peanut butter, you can either start your own supermarket, or target the mom-pop stores and hope for the best.
I think this kind of stuff is highly regressive. The Internet was this place where you succeeded on your own merit and not because you pay-to-win. A place where a tiny company like Google was able to sell their service because it was on the same playing field as lycos/yahoo/altavista. If accessing Google cost you money while lycos/yahoo/altavista were free, nobody would have ever tried Google. And without enough people searching and clicking on links there will never be enough seed data for a good ranking algorithm to work.
The supermarket is a good example. That's already how it is, all the time, and yet we still get incumbents. Have you seen how many different kinds of jams, jellies, and peanut butters have taken hold? Yes, it's a challenge to be the new guy on the block, but that is just the nature of the beast. Now, if Jiffy paid supermarkets not to stock other brands of peanut butter, that would probably be anti-competitive.
If accessing Google cost you money while lycos/yahoo/altavista were free, nobody would have ever tried Google.
We can't know for sure, but IMO this is totally not true. The cost for one search worth of traffic is tiny, and their results were superior.