What you are after is a "streaming" setup. From there, you can choose to actually stream live, or only record to your SSD, or both. If you record to your SSD, from there you can upload it to YouTube as-is, or further edit it and upload it later.
The basics of the system is:
1) A camera that can capture optically what you are after. An SLR will give you the most options, because the lenses are interchangeable. You can get used ones on ebay for a few hundred. Or, you can get a dedicated camcorder. Two things you will have to watch out for is the camera you select has "clean HDMI out", and it does not auto stop recording every 10 or 30 min (there is a law that if a camera records over 30 minutes, the tax is higher).
2) You don't use the camera's SD card. You bypasss it, and the camera is hooked up directly to your computer. You start and stop the recording from your computer, and never have to touch the camera. It stays on 24/7.
3) The connection from the camera to the computer is via HDMI cable. All cameras have an HDMI out, within the past 10 years. To get the HDMI cable to connect to your computer, you need an HDMI to USB3 adapter (if on a PC), an HDMI to thunderbolt adapter (if on a Mac), or an HDMI to PCI adapter (if on a desktop). They cost from about $100 to $500.
4) To take the camera's HDMI signal and convert it to something usable in file size and bit rate, you need encoding software. There are some free ones, and some paid ones.
I did all of the above and recored to my Mac's SSD for the past 5 years (I never streamed live). The videos I wanted to share I put on YouTube. The whole thing is pretty complicated, as there are many, many separate things you have to figure out. From the optics for pool, to the physical connections, to the encoding software, to a computer powerfule enough, etc etc. The above will get you going.
Here is a good video showing some of the basics. This guy's channel is really good for equipment and how-to for live streaming.
https://www.youtube.com/watch?v=5SNBdAL6sxQ
I believe the setup you were looking at comes with an encoder, and you would use that instead of the software in step #4 above.