How do I convert a British biscuit recipe to a moister American style cookie?
You will need to make some experiments if you need to add something or to change an igredients. 

Cookies are chewy because they are moist. Easiest trick in the book - bake the cake for the first 1/10 of cooking time with temp 20% higher than in recipe WITH a bowl of water. 

Other methods:


split sugar into two types. White and brown sugar. Let say
50/50.  Brown sugar have molasses so it have more water in it.
Try adding soda. What you wrote down is very similar to
black cake I made with the change of oil for butter and few tbs of
soda. Mine is not very chewy but I prefer to add more cocoa than
chocolate.  Soda help keep the moisture in.
lower the amount of flour or/and let the dough rest for a
bit to develop gluten.
add wetness - so add extra egg white, or a spoon of
yoghurt, or some water.