Revert of Convert ChromeSyncShell to use ChromePublic infrastructure (patchset #7 id:120001 of https://codereview.chromium.org/1282603005/ )

Reason for revert:
broke ChromeSyncShell build.
http://build.chromium.org/p/chromium.linux/builders/Android%20Arm64%20Builder%20%28dbg%29/builds/22336/steps/compile/logs/stdio

Original issue's description:
> Convert ChromeSyncShell to use ChromePublic infrastructure
>
> Several test fixes are included to support this change.
>
> Note: This CL only provides a GYP implementation (no GN). This is not a
> regression from the previous state.
>
> BUG=510211
>
> Committed: https://crrev.com/62ca3f0326203cca221bba6f0ee038ff292ecc66
> Cr-Commit-Position: refs/heads/master@{#344128}

TBR=jbudorick@chromium.org,newt@chromium.org,pvalenzuela@chromium.org
NOPRESUBMIT=true
NOTREECHECKS=true
NOTRY=true
BUG=510211

Review URL: https://codereview.chromium.org/1285373007

Cr-Original-Commit-Position: refs/heads/master@{#344137}
Cr-Mirrored-From: https://chromium.googlesource.com/chromium/src
Cr-Mirrored-Commit: ec748bc5560f56d838178b07313e59bd4136f7ee

all.gyp

@@ -87,8 +87,8 @@
                 '../android_webview/android_webview.gyp:system_webview_apk',
                 '../android_webview/android_webview_shell.gyp:android_webview_shell_apk',
                 '../chrome/android/chrome_apk.gyp:chrome_public_apk',
-                '../chrome/android/chrome_apk.gyp:chrome_sync_shell_apk',
                 '../chrome/chrome.gyp:chrome_shell_apk',
+                '../chrome/chrome.gyp:chrome_sync_shell_apk',
                 '../remoting/remoting.gyp:remoting_apk',
               ],
             }],
@@ -875,9 +875,9 @@
                 '../android_webview/android_webview.gyp:android_webview_test_apk',
                 '../android_webview/android_webview.gyp:android_webview_unittests_apk',
                 '../chrome/android/chrome_apk.gyp:chrome_public_test_apk',
-                '../chrome/android/chrome_apk.gyp:chrome_sync_shell_test_apk',
                 '../chrome/chrome.gyp:chrome_junit_tests',
                 '../chrome/chrome.gyp:chrome_shell_test_apk',
+                '../chrome/chrome.gyp:chrome_sync_shell_test_apk',
                 '../chrome/chrome.gyp:chrome_shell_uiautomator_tests',
                 '../chrome/chrome.gyp:chromedriver_webview_shell_apk',
                 '../chrome/chrome.gyp:unit_tests_apk',