When the book was written limit hold'em was the dominate form of hold'em, with significant differences then the way the game is played today. No limit was a rare game. I worked at the mirage from 90 to 98, and dealt no limit once, to Stu Unger and another player. S&M at the time probably did not even consider much what the differences were, and if they did they considered them in the context of a no limit game without a cap on the buy-in, and not the super aggressive short stack way that it's played today.
Keep in mind that hand rankings in the original form where based entirely on math, that is to say that AA wins X amount of time, KK wins X amount of times etc. Then when you start adding variables to this with the number of players and rank them by expected value, rather then just how often as a percentage a particular hand holds up against a particular number of random hands, the rankings of hands start to change. The first hand rankings were calculated by hand, as computers became available and more powerful the hand rankings have become more elegant. The S&M ranking you have was done late 80's, like 87 or 88, on best an old 286 or something rather tedious to program and run. It has been revised since.
Consider a hand like AK against say a pocket pair like 99. The pair of nines is a better hand, has a better EV then AK whenever your playing head up with just one other player. I think it is something around 52% for 99, 48% for AK. That is a general number and varies a little bit with what suites each of the players hole cards are in relation to each other. You add another player to the mix with something like J-10, and the EV of 99 goes down roughly by half and the EV on AK goes up, AK wins at a slightly diminished percentage, but is now getting 2 to 1 on the money rather then 1 to 1, which makes AK fairly profitable in the three way pot, and 99 a loser with EV. (There are huge variables outside of the scope of just hand rankings, what the game is like, what your particular opponents are likely to do etc.)
So one of the simple differences in a hand ranking for no limit is that the average number of players seeing a flop in a typical no limit game is lower then the average number of players seeing a flop for a limit game. IF I would venture to put a number on it I would say about 1.5 more players each hand see a flop in limit then do in no limit. The result at any rate is a general upgrading of the EV of pairs at the expense of the rating of A-Face hands for a no limit rankings.
Keep in mind that the hand rankings, any hand rankings are just guideline. The particular S&M hand ranking your looking at from Texas Hold em for advanced players will suit a beginning player just fine as a starting point. Poker is not so much about hands, as it is understanding about when your particular hand is worth playing, and that is determined more by the variable of the hand your in on any particular round.
To demonstrate what I mean lets go back to 99 head up against AK. If you are the player with 99 and read someplace in a hand ranking that 99 is favored over AK head up, you may decide to always play 99 head up. So a player raises into you with AK and you call, determined to call all bets, because 99 is favored. You will have a negative EV, because the biggest variable is that smart players bets when he is ahead, folds when he is behind, and dumb players always call and check when unsure. 55 is better then AK head up in the hand rankings, but you need to be a really seasoned player to play fives head up profitably against AK, and how profitable those fives will be depends on how well your opponent plays.
S&M from what I understand have revised their hand rankings over time. Don't know if these revisions made it into later reprints. There are also other rankings out there for no limit and limit. To me they are not a big deal, but great for beginners. There not gospel to any seasoned poker player. The main part of what a poker players learns through experience is to think critically about any particular hand to come up with the best EV for that hand, that kind of thing does not really fit into a hand ranking chart.