It is impressive that enough old commentaries exist to allow citation of a commentary on a related game, thanks John!
Robert: I have spent years trying to tell you that there's a massive amount of stuff available. Throughout the 20s and 30s every Oteai got a long commentary, very often from Shusai. Nowadays all the space goes on variation diagrams. In those days readers had hair on their chest - even the women - and could read commentaries full of Black A, White B etc based on diagrams with 100 or more moves.
On top of that, because pros were not as spoilt as they are now, they did almost all the work of commenting and article writing themselves. So all the articles are from the horse's mouth, and not the other end.
It remains unclear why the 4-space extension would given White "richer possibilities". Different possibilities for sure, but why richer? Black's richer invasion possibilities are hardly discussed.
You've got to do two things: one is not to over-analyse and the other is to read what is written. The commentary said it was the game that got richer possibilities, i.e. both players, not B or W.
As to "richer" it just means a wider variety. Don't read too much into it.
On top of that, it is just my top-of-the head choice for a Japanese word, and may not be the best choice. The word in question is "hiroi", which usually means "wide", but that doesn't fit here. It's a very common word and you must have come across it many times in English translations, but probably didn't notice it much because it would often be (mis)translated as "wide". I have discussed it a bit in the Shuei game commentaries, but it needs (dare I say it) wider exposure.
Although common in commentary texts, hiroi is rare in books and articles. I think I have seen only one book that discusses part of it, maybe by O Meien but I've forgotten. It's like amashi, also very common in commentaries but rarely discussed in depth. The most I've seen on that is as part of articles, e.g. on technical terms.
I think there's a good reason for that, but I am now entering the realms of speculation. The reason is that these are concepts that can only be sensibly discussed once you know all the basics inside out, and so can apply only above about 6-dan amateur. And pros rarely write for other pros. In fact, I deduce that, leaving aside physical and psychological improvements and the gradual build-up of experience and keeping up to date, these two things are the most important aspects a low-dan pro learns as he moves up the dans. Nowadays, however, dealing with a hiroi game is probably more noticeable because weaker players have more or less learned to avoid suffering amashi strategies, and so we see fewer example than in the past, with the recurring exception of that caricature of amashi, the one-weak-group strategy.
Hiroi essentially describes a game that is rich with (= full of) possibilities. It means a game with a lot going on. However, it does not mean mayhem. Players who play a hiroi game have to have that an attribute similar to the controlled aggression taught to London bus drivers and F1 drivers, or to the ability to go to the limit but not beyond that top rock climbers have. By its nature such a game is likely to benefit a stronger and/or more experienced player - typically White in no-komi days.
Your remark about White playing hamete in no-komi days is a bad misuse or misunderstanding of the word. A pro only extremely rarely tries to trap a fellow pro with a trick move. However, he will very often use hiroi moves.
Both hiroi and amashi strategies are used even in komi games, though as I said actually achieving amashi is quite nowadays.
For an amateur to learn to play hiroi moves is difficult not just because of the need to master the basics first. Another factor is that he may not get to play stronger players enough, either on level terms or giving a handicap. But in no-komi days this was common. At B-W-B handicap, a weaker player got to play a stronger player with White and no komi in one out of three games. This was a marvellous opportunity to challenge him to a hiroi or amashi game, and it's part of the reason that players like Kato Shin believed that no-komi go should have been retained. The Japanese have a lovely way of describing this, borrowed from sumo wrestling. They refer to it as "borrowing the chest" of a stronger person so they can practise pummelling him. This term is fairly common in go, but for obvious reasons it usually can refer only to pros.
Again, don't try and over-analyse any of that. I've typed it with one eye and two ears on the TV as the general election results come through, and it may all be gibberish, but I'm confident there will be a grain of truth somewhere.