Yes, primarily the "cents" given in my explanation above are expressed in €, it may cost a little bit more in $. But it's not so many expensive and it the game for Dapp. Secondarily, concerning your question, yep too!
You don't win eth as rewardsfor sure, but for all battle (won or lost) your mons gained experience points (they are more strong and can evolve or lay eggs). In addition, when you win a battle (anytime, even if you don't make an attack yourself and that just an other player attack you) you will won 0.2 emont (the infuel game currency). Those emont will allows you to pay for mon, stamina or adventure mode.

Keep playing