The answers I have aren't all that conclusive but here goes:
The retail version you buy in shops is what we call FPP: Full Packaged Product. This is a specific SKU (stock keeping unit - essentially a specific product or set of products bundled together) that contains both sets of media, 64 and 32 bit. The link that Paul referred to -
http://www.microsoft.com/windows/products/windowsvista/editions/64bit.mspx - is aimed at this particular sku.
However the sku you folks have is a special custom sku that we created for the competition, and there is no process set up for it as a result.
What does this all mean? Feel free to try order the 64 bit version by entering your product key on the relevant screen by following the link. It may be fine, it may not, unfortunately we can't guarantee it either way.
As for the OEM vs Retail question: for the purposes of installing it on alternative hardware (ie removing it from one piece of hardware and installing it on another) you can consider this as the retail version ie it's ok to do that.
Hopefully that sheds some light on the situation. If/when I hear more I'll let you know.