XSLT: XML to XML with nested attributes

As per @michael's comment, it seems that your sample isn't really representative (since Rooms can have multiple Doors), and you will also need to determine the logic on how to project an aggregate boolean representation of all door check states onto the parent Room.

Here's an example of mapping with multiple Doors, with the logic that all doors must be check='true' in order for the Room/@check to be true:

<?xml version="1.0" encoding="utf-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Transform">
    <xsl:output method="xml" indent="yes"/>

    <xsl:template match="/Level">
        <Result>
            <Listing>
                <xsl:apply-templates select="Stage/Room"></xsl:apply-templates>
            </Listing>
        </Result>    
    </xsl:template>

    <xsl:template match="Room">
        <Room check="{count(Door[@check='false']) = 0 and Door}">
            <xsl:apply-templates select="Door"></xsl:apply-templates>
        </Room>
    </xsl:template>

    <xsl:template match="Door">
        <Folder id="{../@id}" weight="{@weight}" color="{@color}"/>
    </xsl:template>
</xsl:stylesheet>

Input Xml

<Level>
    <Stage>
        <Room id="1">
            <Door color="Brown" weight="5" check="true"/>
            <Door color="Purple" weight="7" check="true"/>
        </Room>
        <Room id="2">
            <Door color="Green" weight="7" check="false"/>
            <Door color="Orange" weight="4" check="true"/>
        </Room>
        <Room id="3">
        </Room>
    </Stage>
</Level>

Output Xml

<?xml version="1.0" encoding="utf-8"?>
<Result>
  <Listing>
    <Room check="true">
      <Folder id="1" weight="5" color="Brown" />
      <Folder id="1" weight="7" color="Purple" />
    </Room>
    <Room check="false">
      <Folder id="2" weight="7" color="Green" />
      <Folder id="2" weight="4" color="Orange" />
    </Room>
    <Room check="false" />
  </Listing>
</Result>