I believe the issue is that the sensor in that camcorder is not all that good by today's standards. According to that camcorder's user manual, it records video in NTSC or PAL format. Even if we associate HDMI mostly with HDTVs, and with monitors, those are lower-resolution formats from before the HDTV era.
An online user manual contained these specifications:
Image device:
3.1 mm (1/5.8 type) CMOS Sensor
Recording pixels (photo, 16:9): Max. 9.2 mega pixels
Gross: Approx. 2 510 000 pixels
Effective (movie, 16:9)*4: Approx. 2 290 000 pixels
Effective (photo, 16:9): Approx. 2 290 000 pixels
Effective (photo, 4:3): Approx. 1 710 000 pixels
An APS-C sensor would have a diagonal measurement of about 28 mm. A 35mm full-frame sensor would have a diagonal measurement of about 43 mm. So you can see that this camcorder's sensor is very tiny compared with those on dedicated "system" cameras. The less sensor area there is to collect light, the more likely it is that there will be noise due to inability to collect enough of it.
All of the effective resolutions are just a little bit above – or a little bit below – 2 megapixels.
Small sensors do allow for smaller lenses (including lenses with very wide zoom ranges), which probably one of the reasons Sony chose to use such a small sensor.