I don't think there is a way to specify a "pure" keepout area in EasyEDA Std but there are other several ways to achieve what you require.. One way is to create a closed loop of track with a unique netname that is no used anywhere else on the PCB to define a keepout area. Others are to create a pad or a solid region with a unique netname to define a keepout area. These should keep tracks out during manual or autorouting. In each case you then delete the keepout defining shape after routing is completed and checked before generating the Gerbers and submitting the board for fab. For purely manual routing  you can just jot place any tracks in the required area.

You may be able to create the keepout area using a solid region set to No Solid with a unique netname and not have to delete it after board routing completion. Try it out on a simple dummy PCB design and check the Gerbers. :)