How to open an URL in Chrome Incognito Tab by launching the Incognito Activity?

It seems it's impossible, as per the answer of @bmdixon :

I don't believe this is possible. According to this Reddit post, it is not possible when writing an app as the Chrome code ignores the request if it is not Chrome initiating it, so an app or user cannot trigger the incognito tab. I assume the same applies when trying to launch the activity 'manually'.

So what these are doing, is checking whether the intent should be ignored based on whether it is the user or chrome performing the action. They make this determination based on whether there is a token from a signed Google app. So unless there is a way to trick find that token and figure out how to attach it to Tasker I don't think it'll work.