You must love that channel more than I love Allison's.
There are lots of review channels, like this one:
Or this:
Or one of my favorite channels (just not regarding the Babel episode):
Or oodles of others.
Those all only go so far, and it takes a lot longer to whip up a view of any style, regardless of how few camera jump cuts or other effects, than to write up something.
So here's my take on the story along with the takes of everyone else responding in this thread:
I've not seen JtB in several years. The last I had watched it, it felt like proto-TNG in some ways with greater emphasis on drama. Yet doesn't fall into generic soap opera, that's how good DC Fontana was. It's not my favorite tale of season 2, but it's nowhere near the worst - it's in the top third of the season for sure. But I'll put "Friday's Child" above it... Fontana rarely wrote a clunker, but I'm straying:
This episode does do a slight retcon from an early episode where Spock talks of a distant ancestor marrying his human (WHMHGB, the second pilot), but fast forward to the end of 1967 and now said ancestor is his actual father. IMHO it's worth it as it tightens up the Trek universe without doing anything egregious* and adds much to Spock (and Sarek). The real fun is explaining why Spock acted so out of character, despite this technically being a pilot episode that was chucked into be aired to save on costs as the show was very expensive for the time.
* especially as this is TOS and coming up with ideas by the seat of their pants on the fly and improvising as they had no "series Bible" or whatever the vernacular is...
I say "proto-TNG" as this was still TOS, where Gene R. had to make changes so that the suits would greenlight it. ("The Cage" even feeling far closer to TNG than TOS ever had.) So obviously there's some action and fisticuffs and a dogfight despite never getting to see the other ship until TOS-R rendered one.
The story has two new alien creations, the Andorians and Tellurites. The costumes may have been reused in later TOS episodes but the species were never expanded on (a rarity for TOS, where the most we got were both Klingons and Romulans returning and only to say how they're "warrior species". TNG definitely brought in more nuance to many species, even if it often compartmentalized one element of the human condition per species for "easier digestion" or whatever phrase you'd want to use. TOS was more situational and macro-level than "navel-gazing" or whatever phraseology fits better anyhow. Which isn't bad, TNG embraced and made most of it good.)
Also, "retro" technically means a recreation/imitation of something of an older style or time and his presentation doesn't fit that in the slightest. "Review of a vintage episode" seems more apposite. But "vintage" generally pertains to fermented grape products, so "antique" may be a better description. Then again, there's no de facto description for that regarding how long ago (25 years for some items, 100 for others), so "vintage" does work... especially as it's easier to find "vintage television shows" rather than "antique television shows" (of which searches often bring up completely nonrelated results, isn't that peachy?) Then again, "vintage televisions shows" ranges from "Gilligans Island" (and stuff before) all the way up to "3rd Rock from the Sun" (1996).) Ah piffle, it's "classic television shows", that works the best by far.