My adobe saga is ongoing. I received a further email today, which fails to address my point, and is encouraging me to go around in circles with my correspondence to Adobe.

Thank you for contacting Adobe Customer Services.
We guess your query is to amend the EULA policy, unfortunately that is not possible for now, may be in the nearest future, please stick to the policy, only install on your PC or other wise buy a full version flash media Server which you can install any where you like.
Should you require any further information, please do not hesitate to contact us.

Although a side-product of my correspondence may be that the EULA for flash-player may change (or be made clearer) - my main concern is whether or not it is legal for me to use the flash-player on my initially-a-'Media Centre'-but-now-a-PC Computer.

As identified quite correctly by popey in #ubuntu-uk - there's no defintion for "Media Centre PC" - therefore I shouldn't be worried on this point.  It was my paranoia, rather than anything specifically in the EULA which led me to think I was running a "media centre."

However, reading through section 3.1 of  the EULA makes interesting reading. If we ignore the "examples list" (in italics) - then it becomes quite clear.

3.1  Web Player Prohibited Devices. You may not Use any Web Player on any non-PC device or with any embedded or device version of any operating system. For the avoidance of doubt, and by example only, you may not use a Web Player on any (a) mobile devices, set top boxes (STB), handhelds, phones, web pads, tablets and Tablet PCs that are not running Windows XP Tablet PC Edition, game consoles, TVs, DVD players, media centers (excluding Windows XP Media Center Edition and its successors), electronic billboards or other digital signage, internet appliances or other internet-connected devices, PDAs, medical devices, ATMs, telematic devices, gaming machines, home automation systems, kiosks, remote control devices, or any other consumer electronics device, (b) operator-based mobile, cable, satellite, or television systems or (c) other closed system devices.

However, I do feel quite silly in pursuing what is now a dead end.. therefore I address Adobe with the following.

Thanks for letting us use flash-player on Linux - but please make the examples list more Linux (and even apple..) friendly :)