Don't use backgrounds. Use ImageView (with RelativeLayout) and set the ScaleType property of the image view as you like. You can set a scale type that will keep the aspect ratio of your image. Also, please note, in cases where you don't want the image to scale, 9patch is useless. The all purpose of 9patch is to let you control how the system scales your image (mostly used for buttons and backgrounds of ui controls).
Your layout (removed some of the elements):
<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
android:orientation="vertical" >
<RelativeLayout
android:layout_width="wrap_content"
android:layout_height="wrap_content">
<ImageView
android:layout_width="fill_parent"
android:layout_height="fill_parent"
android:scale_type="centerInside" //Do whatever scale type you like
android:src="background image goes here"
/>
<LinearLayout
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:orientation="vertical" >
<TextView
android:id="@+id/activity_win_textview_congratulationText"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_gravity="center_horizontal"
android:layout_marginTop="@dimen/activity_horizontal_marginXExtraWide"
android:gravity="center"
android:text="CONGRATULATION!\nYOU WON!!!"
android:textColor="#FFF"
android:textSize="@dimen/textSize_XLarge" />
</LinearLayout>
</RelativeLayout>
</LinearLayout>