Tab gravity only effects MODE_FIXED.
One possible solution is to set your layout_width to wrap_content and layout_gravity to center_horizontal:
<android.support.design.widget.TabLayout
android:id="@+id/sliding_tabs"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="center_horizontal"
app:tabMode="scrollable" />
If the tabs are smaller than the screen width, the TabLayout itself will also be smaller and it will be centered because of the gravity. If the tabs are bigger than the screen width, the TabLayout will match the screen width and scrolling will activate.