One possible solution is to use Appodeal without Google Play Service.
But before, there are two tutorials that recommend reading:
1) How to install Cranberry's Google Play Games plugin (Cordova)
2) Simplest Appodeal Ads Tutorial
So, the steps to do.
Configure the Plugins
Cranberry's google play games plugin
First, select on the Projects Bar (default to right) the PhoneGap Game Plugin. Then, on the Properties Bar (default to left), you will find the text-box named Android Google Play App Id. Here you need to enter the app id found in your Developer Console. Like in the picture below:
Then select the Appodeal Plugin. In the text-box named appKey you need to past the Application Key (the key under the app name in this page).
Export via Cordova
Now you can export the game. But, it's important!, before unchek minify script.
Configure Intel XDK
Add Plugin: Cranberry's google play games plugin
Now you can add the plugin into Intel XDK. First the Cranberry's Google Play Game. Open Intel XDK -> Open project (assuming you have one already) -> Plugin Management -> Add new plugin -> Third-party plugins and in the Plugin-ID field, you want to type in
When Intel XDK prompts you to add the APP ID, just paste your Google Play Game Services app ID in there
Add Plugin: Appodeal
Now the Appodeal Plugin. In Intel click on the button to add a 3rd party plugin and then in Git Repo write:
The last step: edit the intelxdk.config.additions.xml.
You do this by clicking the DEVELOP tab and opening the intelxdk.config.additions.xml file. Find this code:
<intelxdk:plugin intelxdk:name="https://github.com/cranberrygame/cordova-plugin-game --variable APP_ID='YOUR_GOOGLE_PLAY_GAME_APP_ID'" intelxdk:value="https://github.com/cranberrygame/cordova-plugin-game --variable APP_ID='YOUR_GOOGLE_PLAY_GAME_APP_ID'" />
and remove it.
Then find this other code:
<intelxdk:plugin intelxdk:name="https://github.com/appodeal/PhoneGap-GooglePlayServices.git" intelxdk:value="https://github.com/appodeal/PhoneGap-GooglePlayServices.git" />
and remove it.
Save (CTRL + S or file>save) and move to the Build tab, build for android and ... the game is ready for Google Play Game and Appodeal Ads.
You will need to remove the code every time you export it from Construct 2, since the file gets replaced with each exportation.