You could try to split on everything but the content and then remove the empty elements in the array.
s="<<<<((((sports====1000))))((((librarys====2000))))>>>>";
s.split(/[<()>=]/).filter(function(ele){if (ele!="") return true});
=> ["sports", "1000", "librarys", "2000"]
This is kind of a hack and since I don't know the syntax of your text this might or might not work out for you.
Yet another hack:
s="<<<<((((sports====1000))))((((librarys====2000))))((((no_value====))))>>>>";
arr = s.replace("====)","====nil").
split(/[<\(\)>=]/).
filter(function(ele){if (ele!="") return true});
var res=[];
for(var i = 0; i < arr.length; i+=2) { res.push([arr[i],arr[i+1]]); }
res
=> [["sports", "1000"], ["librarys", "2000"], ["no_value", "nil"]]