Is it the transport or DAC that enables HDCD/Red?

Yes, HDCD capability is (or isn't) in the DAC. All transports supply the information off the disc, Redbook or HDCD. DAC's themselves almost universally employ a D to A chip of some kind. Some are better than others, but if they DON'T do HDCD, then the extra digital information for HDCD processing (of an HDCD disc) is disregarded (basically dumped.) Otherwise, on HDCD implemented DAC or CDP, a Pacific Microphonics chip is used which WILL recover the HDCD info. The problem is that the Pacific Microsonic chips aren't the highest quality, which is why most hi-end DAC's/players don't do HDCD. That is, except for Mark Levinson, which got permission to make THEIR OWN high quality HDCD decoding chips under additional license from Pacific Microsonics.

One other (high end) exception is Wadia. Unlike Mark Levinson, they do not use a custom HDCD chip. In fact Wadia DAC's don't use ANY D/A "chip" in the usual sense. Wadia uses their (claim to fame) patented "Digimaster" decoding software. Basically, Wadia DAC's are really high speed computers using the proprietary software to decode digital audio data. For that reason, the HDCD information is not dumped, but processed by the software. So although you won't get an "HDCD" indicator light on a Wadia, you WILL get the best HDCD perfomance (I've heard.) Is it better than the Levinson's custom HDCD chip. I haven't heard the Levinson, but the Wadia HDCD reproduction is truly amazing.
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Plenty of DACs that decode HDCD, unfortunately they are all a few years old. Besides those mentioned above, Adcom, PS Audio, and Proceed come to mind.
A well mastered HDCD disc played through a quality HDCD player or DAC is superb. One of my favorites is Beck's "Sea Change." Joni Mitchell "Blue" and "Court And Spark" are a couple other great ones.

The reason high-end players/DACs tend not to decode HDCD today is strictly based on cost -- licensing fees.

Yes thanks to Microsoft's purchase of PMD.
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I believe the recently released BADA is a DAC that does HDCD.