Does "Microsoft now bundles Google's browser engine" really scream "won the browser wars" to you?

Do you not think the settlement requiring APIs be opened up helped enable Chrome at all?

No, because the post-settlement era was actually the era of consolidated IE dominance. Chrome only started because MS, in their (unbroken by the FTC) dominance had sat around doing nothing for the web, which was bad for a web-based company like Google. Chrome also avoided using platform APIs because they wanted to be cross-platform.