We (BrowserStack) are not sure why you are facing issue with respond.js. We tried sample test page, which works as expected.
Your url, our test with IE8 VMware VM's and BrowserStack IE8 report the same result. Local IE8 VM BrowserStack IE8
We went ahead to try to make it work like chrome. Enabling setting "Access data sources across domains" makes it work something like below, not exactly like other browsers like chrome.
Let us know for any further clarifications.