Does that mean that I cannot use any other services that have monetization for my app?
IANAL and I'm not too familiar with Appodeal, but it sounds like they are restricting the use of their services (ad mediation) in apps that offer monetary value to the end users. An example of an app that has real monetary value (in my opinion) would be something like Google Opinion Rewards -- although they may actually mean monetary value only, rather than credit or points.
If you are considering using their services, you should probably contact them first (firstname.lastname@example.org) and clarify exactly what that statement means, since it could impact your use of the services as well as limit your options.
This statement is from https://www.appodeal.com/terms-of-service . It's for publishers. But if I publish my apps, does this mean I fall under this rule?
In my non-lawyer opinion, yes; if you agree to their terms and sign on to use their ad services in your app, you would be subjected to all of their terms that affect publishers.
I was thinking of using their ad services but if later on, I cannot add in-app purchases than it's not what I want. Is that the case?
It doesn't sound like that statement restricts the use of in-app purchases by a publisher. From the wording, it seems like it affects offering monetary value to the user (rebate, cash, etc.) rather than offering something they can purchase. But again, I would contact Appodeal and clarify that before agreeing to anything.