''Mandatory'' / ''Required'' fields only need to have values populated on CREATION. You do not necessarily need to MAP a field to them.
Also, in QC, it is possible to uncheck the ''Required'' flag on a system or custom/user field (Tools/Customize area in QC project). This should be possible in endpoint2 as wel.
The link's mapping picks up on these settings and there is nothing you can do other than provide a field that maps to the ''mandatory'' ones or a CONSTANT that fills in a value (it would be a static/initial value).
Also confirm in QC and Endpoint2 that ALL of these fields are in fact Required/Madatory and see if you really need them to be -- it could just be an over-zealous Admin setting them that way.
If you need to ''satisfy'' a required/mandatory field as part of mapping, you can, for instance, use the Add Constant Value button to set an INITIAL value to the field.
We do this often with ''Issue Type'' and ''Project'' fields in JIRA as endpoint2.
When we say ''creation'', this is when a new record is created during Sync into the ''other'' endpoint (i.e. sync senses a new record in QC, it then tries to create a corresponding NEW record in endpoint2 -- it then must satisfy the MANDATORY fields only during this creation).
It is a BAD idea to try to cover ALL possible fields (required or not) with mapping -- everyone in the ''other'' tool really likely does not care about the values of them -- ALSO it is a really bad idea to try to do bi-directional mapping on too many of them. Mostly, you just need to report the current value to the other endpoint - and really don't need people to edit/change the value from both sides -- this makes it harder to establish the mapping.
If you just need to report the current value, mapping to a target custom field of type STRING will usually work just fine.