Is there a way I can share test cases that I created to other members in my team so that they can run the test in there system. We are not using Git or any other version control system. If I export from Katalon recorder in groovy format will the object that associated with the test case also be exported?
Git or any other version control system is the good solution I strongly suggest you and your team doing that. In case we do not have the settup, I think the work around solution is that you zip all the project and send to your members, so that they could use another instance of Katalon Studio and open it.
Normally, the zip for whole project is a few MB, so it is possible to do that.