The guy in the link is speculating. While capacitors do lose their charge over time, it varies per type. For them all to be completely empty every time the computer sits idle, there has to be a drainage circuit specifically designed to remove the charge from them or they need to naturally leak into the circuit, which isn't guaranteed.
While I've been running Gigabyte for the last twenty years, almost exclusively, and have the same board as the OP, I will say, I don't have a definitive answer for the behavior, but I suspect it has nothing to do with capacitors. I only see the behavior when parts are close to limits, as in overclocking or when 1600 MHz RAM was still a bleeding edge component and the initial modules weren't the most stable.
Gigabytes BIOS on startup actually gives insight as to what is happening, if the case is extreme enough. It is not just a one-time shut down and power up for the motherboard but it will actually do it many times if necessary. If the BIOS is configured in such a way that something, such as the CPU or RAM completely fail to POST, the motherboard powers off, then powers up again with slightly tweaked settings for the part. I've witnessed a motherboard go through this up to four times. After the fourth time it actually powered on perfectly fine, and had a message on the POST screen that basically said, gee whiz, your system is overclocked and unstable, but really means, the settings chosen for the first few boot attempts didn't work.
While the bad settings will remain in BIOS, it's nice to know that there is a safeguard in there that is capable of some minor recovery effort in the case of a failure to boot.
My speculation is that upon initial power on, a component in your system is barely falling outside of a specification, such as the RAM modules, which may need a slight few +mv tweak at this point, or may be running with the wrong profile and thus timings.
Edit: Capacitors can charge and discharge in less time than it takes a motherboard to perform a momentary power cycle. There is also no valid reason to charge them, as even when modern PCs are powered off and not sleeping, they have voltage supplied to the motherboard. The machine would have to be disconnected from the wall or have a physical disconnect switch on the PSU to prevent power to the motherboard.