HDMI (v1.4) alone is capable of providing power to the Chromecast, pin 18 is specced for +5V/50ma.
Not every TV/monitor supports this since there aren't that many devices out in the field that utilize HDMI power, but if your TV does provide power over the HDMI port then the Chromecast can get everything it needs just from the HDMI port.
Using your Chromecast this way puts you at a disadvantage with many TVs. My TV only provides HDMI power when the input is selected (this may be per the spec) but that eliminates Chromecast's 'switch the input automatically' feature.
Not every TV/monitor supports this since there aren't that many devices out in the field that utilize HDMI power, but if your TV does provide power over the HDMI port then the Chromecast can get everything it needs just from the HDMI port.