The higher the level of the weapon and the level of char, the higher is the Atk. Str does add atk, but is not necessary. Lets make a fast calculation on lv 10 cyclone’s damage:
At level 280, you can easily get 1800 atk with a good 2H weapon and warcry+gung ho+DoV (even without frenzy). Lv10 cyclone inflicts 1000 damage per hit, supposing that it does 26 hits by using the overheat 2x:
Full dex lv10 cyclone -> 280026 = 72800 without crit; with high crit = 728001,4~1,6 =~ 109200.
With full STR at lv280, you can get something like 500 STR, that is doubled with DoV, giving something around 1000 bonus atk.
Full str lv10 ciclone -> ((1800+1000)+1000)*26 = 98800.
Even just without crit, your 500 STR only increases 27% of the damage, while crit increases from 72800 to 109200 (34%).
Just remember that high level mobs have something like 100~150 crit resist and cyclone have the highest scaling in all swordsman skills. 100~150 crit rate will do nothing on them; but a full dex 350 crit rate will hit very hard.