"Unsupported" project type doesn't really mean that you can not use EurekaLog with your project. It just means that EurekaLog doesn't have appropriate template for your project and you'll need to write some code. Nothing scary.
Basically, you need to find some kind of "OnException"-style event and invoke EurekaLog to handle current exception. For example, VCL and FMX applications have global Application object with OnException event. A console application can use explicit try/except block around code. A IntraWeb application has DoException event in ControllerBase. Many Indy objects have their own OnException events. And so on. Just refer to framework documentation to find the proper event for handling exceptions.
To perform exception handling (processing) - call any of exception handling functions.