Assuming you don't already have the values, as in @Henrik Peinar's answer, you can parse the value from the string, (as long as it follows the conventions in your example).
Here are a couple ways you could do it:
1) Format the string to JSON notation, convert to object, access values
var objOptions = JSON.parse("{" + varOptions.replace(/;/g,",").replace(/=/g,":").replace(/(\w+)/g,'"$1"') + "}");
console.log(objOptions.dialogHeight);
2) Parse out only the value you're looking for using RegEx (my example is prone to errors, so I would do it a bit differently in production. This is just a quick example.)
varOptions.match(/dialogHeight:(\w+);/)[1]
3) Use split to get an array of the name-value pairs, then loop and split those results, testing the 'name' piece until you find the one you want. (I'm running out of time, so I've left off this example)
var dialogHeight = 580; var options = 'dialogHeight:' + dialogHeight +'px;dialogWidth:700px;center=yes;scroll=no';?