As @stpaultim said, this is a bug. You have at least three options to fix this while a new release is prepared:
Option 1: apply a patch
Applying a patch requires some technical knowledge, and "shell access" to your hosting or your local environment. You may be able to find the steps by doing a search on the internet (I will write a rough guide in the next few days in this forum for people who may not be familiar with this process). You can download the "diff" file here, which is basically the permalink to the patch (you can find a clearer formatting done for human eyes here)
Option 2: manually modify the file
Use the links I have in the above option and manually edit the file by changing the lines. You will basically remove lines that have a "-" sign there, and add the ones with a "+" (but be sure not to type of "-" or the "+").
Option 3: download the previous version of Backdrop, and use the old file layout--flexible.tpl.php
layout--flexible.tpl.php will actually work with release 1.20.2. This is not ideal, but it's the easier solution for someone who doesn't want to mess up with the other two options. It's definitely not an ideal solution, as you may be introducing some security risks from previous versions, BUT in this case, that's not the case. You can find previous releases here.