A TV does not require a 16:9 screen to be considered an HDTV. While all HD broadcast content is in 16:9, it's perfectly acceptable to have that presented on a 4:3 screen as letterbox. The only requirement on a TV to be considered an HDTV is to be able to accept HD signals and display them in HD such as 720p or 1080i.
Your HDTV should be able to display Xbox 360 games in 1080i, 16:9 format. Make sure the setting on the Xbox is set to 16:9 and verify settings on the TV for receiving 16:9 content.
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