I think you have it exactly backwards, if I understand things correctly.
It _seems_ like their "UTC Epoch time" is the same thing as POSIX time, but the Google engineer's terminology is all fubar. The reliance on the Proleptic Gregorian Calendar is further proof as that's a reference to a specific algorithm for calculating calendar dates.
POSIX time says that there are precisely 86400 "seconds" per day, which I think implies the same thing as saying there being precisely 60 "seconds" per minute. The logical consequence is, of course, that in neither case is "second" referring to the SI second.
Once you get over the fact that we're discussing different units of time, then you can see that POSIX time is _perfect_ for recording and manipulating civil calendar time. For the purposes of calendar manipulation, you rarely if ever need to know elapsed time in SI-unit seconds. All you care about is easily calculating past and _future_ calendar information. Your power company and credit card companies don't bill you by SI seconds, they bill you by the hour, day, week, or month.
Conversely, in those situations where you want accurate and precise SI-second measurements, you rarely if ever want to convert or display that data in terms of calendar time. When SpaceX sends a rocket into space, the view screen shows elapsed seconds since launch, not elapsed seconds since lunch. That's a big difference.
Interestingly, in neither case do leap seconds matter! They're irrelevant. Leaps second play no part in either TAI or POSIX time.
There are some cases where you want both pieces of information, but I think it's usually a mistake to conflate them and try to shoehorn them into the same units. That misguided practice is behind all the anxiety about leap seconds in UTC time.
It's also worth noting that as clocks become increasingly precise and accurate that the whole leap second thing will fade away. UTC time is based on the fiction that there's an abstract, universal clock in the world that is measurable in SI seconds. There isn't. At some point the needs of routine industrial measurements will enter the realm where relativity governs, at which point the fiction will be laid bare. Calendar time, of course, doesn't rely on that fiction.
The move to uncouple civil time from solar time is totally misguided, IMO, and only exacerbates the improper way that software engineers conflate the purpose and function of various time measurements.