Problem resolved. I didn't expect to find it this quickly. Apologies for somewhat hastely posting about this issue!
I actually solved the issue awhile back, but I believed the solution didn't work because a completely different bug was crashing my app the entire time. So after solving that, I discovered my issue was already gone.

The only thing you need to do to get Google Analytics to work with Google PlayGames is:

1. Install Google Analytics as described in their readme
2. Install Google PlayGames as described in their readme
3. Don't add the 'google-play-services_lib' folder in 'Assets/Plugins/Android', and if you did, simply delete it.
4. Add the following code to GPGSDependencies.cs

svcSupport.DependOn("com.google.android.gms",
"play-services-analytics",
PluginVersion.PlayServicesVersionConstraint);

That should remove the compatibility issue, and allow you to run the code.
Do make sure both plugins work independently first. Otherwise, you might get a problem with one of them, and believe it's about compatibility.

Thanks it save my time

I had a similar issue, and I solved it adding all the Google libs at the same version.

I.

DuskLightStudios your way doesnt solve my problem. I have last version of google analytics (V4) and also last version of google play game service ( 9.34). In editor no problem but in android i took this exception from logging with adb:

java.lang.NoSuchMethodError: No static method zzy(Ljava/lang/Object;)Ljava/lang/Object; in class Lcom/google/android/gms/common/internal/zzab; or its super classes (declaration of 'com.google.android.gms.common.internal.zzab' appears in /data/app/com.HTGames.blinkblock-2/base.apk)
09-29 18:41:40.941 10507 10538 I Unity : at com.google.android.gms.analytics.internal.zzf.zzay(Unknown Source)
09-29 18:41:40.941 10507 10538 I Unity : at com.google.android.gms.analytics.GoogleAnalytics.getInstance(Unknown Source)
09-29 18:41:40.941 10507 10538 I Unity : at com.unity3d.player.UnityPlayer.nativeRender(Native Method)
09-29 18:41:40.941 10507 10538 I Unity : at com.unity3d.player.UnityPlayer.a(Unknown Source)
09-29 18:41:40.941 10507 10538 I Unity : at com.unity3d.player.UnityPlayer$b$1.handleMessage(Unknown Source)
09-29 18:41:40.941 10507 10538 I Unity : at android.os.Handler.dispatchMessage(Handler.java:98)
09-29 18:41:40.941 10507 10538 I Unity : at android.os.Looper.loop(Looper.java:158)

if you have an idea i will be really grateful

just edit AndroidManifest file and set min sdk and target sdk