Getting browser already open error message in Test Execute

Check the following. https://support.smartbear.com/viewarticle/75925/?utm_source=site-search&utm_medium=search-results&utm_campaign=site-search-c&utm_term=checking+if+browser+is+running#_ga=1.206198931.1015556109.1449503065

The above article provides how to check if the browser is still open and to close all open browsers, both from keyword and script tests. Add these steps to you test and see if it helps when running them from TestExecute.