So I have no idea how Miracast works and have no clue if it is possible but i think it would be awesome to use this to accept Miracast from my Nexus 4 and HDMI output to my television. I know that because it has Android 4.2 it should support Miracast output but with how buggy all things Miracast that I have seen are, I would not want to use it for gaming anyway.
If you have a really good Miracast dongle for your TV (definitely not the Rocketcrap one), it's apparently pretty good. I have only tried the Rocketfish version, and while it worked for a short bit, it hiccuped and died a horrible death. The Nexus 4 is horrible for Miracast, so don't use that as an example. That's because Miracast is basically just an MPEG stream sent over a dedicated wifi channel (WiFi Direct). This is why the Nexus 7 can't do Miracast... It doesn't have the ability to have a second channel open at the same time. SHIELD has hardware-accelerated MPEG encoding, so Miracast runs a lot smoother and with less latency. The Nexus 4 either lacks the hardware encoder, or for some reason, doesn't use it.
But to answer your original question: By default, no, you can't turn SHIELD into a Miracast dongle. Technically, it *is* possible, and I've seen it done on similar hardware, but it's not something the device is designed or programmed to do.