Import Tables without Constraints from Schema Export
You are right when stating I thought that by using INCLUDE=TABLE only the tables would be included, but it includes all related objects too. This means that constraints and triggers will be created for you when you use INCLUDE=TABLE when importing.

Possible Solution
If you have the possibility to re-create the dump using the expdp command then you might want to just export the tables of the required schema and use the INCLUDE parameter.

INCLUDE
Purpose:
Enables you to filter the metadata that is exported by specifying objects and object types for the current export mode. The specified objects and all their dependent objects are exported. Grants on these objects are also exported.

exp_include.par
This is basically the expdp parameter file.
FULL=N
...
SCHEMAS=&lt;your_schema(s)&gt;
INCLUDE=TABLE
...

This will create a dump of the required schema and contain only tables and dependant objects.

After you have generated the required *.dmp file, import using the EXCLUDE=... option.

EXCLUDE
Purpose:
Enables you to filter the metadata that is imported by specifying objects and object types to exclude from the import job.

imp_exclude.par
This is the parameter file for the impdp.
FULL=Y
...
EXCLUDE=STATISTIC
EXCLUDE=CONSTRAINT
EXCLUDE=TRIGGER
...

This should result in the tables being imported correctly.
Reference Material

2 Data Pump Export (Oracle Docs)
3 Data Pump Import (Oracle Docs)