更正一下，應該是叫做主謂結構的狀語。

Then took the other, as just as fair,

And having perhaps the better claim,

 

我的理解如下：

 

這個句子的正常結構是應該是這樣的： Then, having perhaps the better claim, (I) took the other, as just as fair.

詩句是為了音韻而改動了詞語的順序。大概意思就是，我也許有更正當（better)的責任（claim），所以走了另一條路，（這行為是）公平的正如（責任是）正當的。