Check out the Charop boards if you wanna know if this is broken or not. In fact, there already is a Slayer optimization guide being made
right here.
Short answer: single stat dependency is nice, but loses out in the long run, what with feats that depend on stats (in the gouge's case, there's Deadly Axe, either critical boost feat (Spear Mastery: Str 19, Dex 19; Axe Mastery: Str 21, Con 17), etc.
Further, a Half-Orc with 18's in Str and Dex can achieve the same thing, taking Weapon Proficiency(Gouge) at first and Master of Arms at 2nd level gets:
+4 str +2 prof +1 level + 1 enhancement +1 feat +1 slayer = +10 vs AC, and damage (no stances) is 2d6 (brutal 1) + 8.
What's more, while it costs him 2 more points at character creation, he will have a much better fortitude defense, and can actually qualify for those critical feats at higher levels.
Also, at heroic level, the 1/2 dex modifier does not really matter that much for damage output. Once the full stat modifier starts hitting +7/+8 ranges, however, he will start to fall behind.
Now, all of this might not be relevant to your campaign - in fact, if I was gonna play in a campaign that didn't go beyond heroic levels, I would probably go for single-stat focus too. But if you're at all planning to reach higher levels, it is decidedly not overpowered and even somewhat suboptimal.