> It assumes you know only how the pieces move and builds step-by-step from there.
Do not get me wrong: TFA is a fine and useful book for an intermediate player but the above claims are overselling it. They are equivalent to telling you that learning the
x ^= y;
y ^= x;
x ^= y;
> Strategy and tactics both are important, but tactics are more important.
> If you're a whiz at strategy but not much good at tactics, you will have trouble winning or having fun because your pieces will keep getting taken.
I beg to differ. You should first learn how to supercharge your pieces by controlling the centre, putting rooks on open files, co-ordinating your bishop pair, keeping a strong pawn structure, etc. Two oldie but goodie books that teach these principles and are available as PDF's are Capablanca's A Primer of Chess [0] and Nimzowitsch's My System [1].
EDIT: memorizing openings ⊄ strategy. I understand strategy as applying good principles regardless of your opponent's moves, and tactics as calculating (mostly) forced move sequences. Also, strategy does not have to be dull. Playing a gambit and attacking Black's f7 weakness is a strategy, albeit one that can hardly succeed without tactical thinking.
[0] https://archive.org/details/aprimerofchess (this particular edition uses the outdated descriptive notation)