Sorry if not proper place, but does this also mean that you can't use another payment option beside theirs? Or there is room like "you can use Paypal if buy from non-mobile version, can't otherwise" ?
The first is correct. It is part of those big license agreements.
If you use Google Play to distribute your product, part of the agreement is that your software will not "facilitate the distribution of software applications and games for use on Android devices outside of the Store." The license also requires: "Developers offering virtual goods or currencies within a game downloaded from Google Play must use Google Play's in-app billing service as the method of payment. Developers offering additional content, services or functionality within another category of app downloaded from Google Play must use Google Play's in-app billing service as the method of payment, except: where payment is primarily for physical goods or services (e.g., buying movie tickets, or buying a publication where the price also includes a hard copy subscription); or where payment is for digital content or goods that may be consumed outside of the app itself (e.g., buying songs that can be played on other music players)."
There is no exception for using paypal or direct credit cards or any other funding method, apart from those exceptions of goods and services or non-app content. Since an in-app currency or ads for another game don't fit the exceptions, you must use their store.
Breaking those rules is a great way to get your apps removed from the store. Since this app is already successful it would be stupid to get the apps removed in a cross-branding effort.
If you sell the product through another store, like Amazon's store for Android, that version can use a different billing system. But the version sold through Google's store must only use Google for IAP.
Apple has similar policies. Any product sold on their store MUST use their IAP mechanism for anything consumed in game.
And naturally Amazon has similar policies, if it was purchased through the Amazon store you need to use Amazon for purchases.