How can a plant become resistant to glufosinate?
Phosphinothricin is a metabolite from the bacteria Streptomyces viridochromogenes which has a protein called phosphinothricin N-acetyltransferase (PAT). This Protein inactivates the phosphinothricin which is the reason why S. viridochromogenes is not dying from it. If you want a plant to be resistant to phosphinothricin you can add the gen for the PAT protein to the plant genom. 
This is also described in this paper about herbicide-tolerant crobs.

An explanation for the resistant goosegrass could be that somehow it got the gen for PAT, maybe by horizontal gen transfer from S. viridochromogenes. 

In your case the publication which is cited in your source contains another possibility. "We hypothesize that reduced herbicide translocation is responsible for resistance to both glyphosate and glufosinate in these populations"