No. It's the same cable that came with the monitor. It might be a metre. Like I said, I am just unplugging the monitor from the MM2012 and plugging it into the MM2018 with the same HDMI adapter attached. I went to the Apple Store and they suggested plugging the computer into a TV with HDMI ports. I did this successfully using a longer cable with HDMI plugs at both ends (no adapter). It worked but I can't use my 55" TV in my office as my monitor.
In other words, the HDMI port and video card in the new Mac mini is OK. I just can't connect the Eizo using the HDMI to DVI adapter. I'm thinking of trying it with a Thunderbolt Mini Display Port to DVI adapter however it might be an issue, software or hardware, with the monitor.