First attempt at showing logs after update did not work, try putting it in a brace group.

linux-game-manager.sh

@@ -60,8 +60,8 @@ if [[ "$home" == "$remote" ]]; then
 fi
     dialog --backtitle "Linux Game manager" \
         --yesno "Updates are available. Would you like to update now?" -1 -1 --stdout || return
-    git pull
-    git log '@{1}..' --pretty=format:'%an: %s'
+    { git pull
+    git log '@{1}..' --pretty=format:'%an: %s'; }
     exit $?
 }