Yes, they do. But it does not change the fact that if the port he was connecting from on his computer was a VGA port, and the port he was connecting to on his TV was the HDMI port, then he was pushing an analog signal on lines that were expecting digital.
The cable he purchased was most likely intended to connect from an HDMI video source (graphics card) to a VGA analog port on a TV or monitor. If this was the case, then the video card would push analog signal over the HDMI port to the TV (this is supported in the DVI standard that HDMI is compliant with). It doesn't work the other way around, though.
This means voltages, frequencies and polarities were quite different than what was expected. At the very least, the port is burned out and the digital signal converter is fine and should work fine if there are other HDMI ports. At the worst, the digital signal converter is toast, which means he's stuck with the analog ports only.