Ok, so there's the issue - the 404 is coming from the gateway, and it's because the URL is wrong.
Tyk Hybrid containers do not use the api-slug, they are pretty raw, so you need to use the API ID to route to the API, and you need to target the gateway directly:
You can find the API ID in the API list in your cloud dashboard.
If you want to use port 80, or use NGinX, then you'll need to do some more work, Tyk Docker Hybrids have nginx installed, but require manual configuration to respect domain names, you can see here:
That the container mounts a confs folder into the sites-enabled folder of Nginx in the container, you can use this to put an Tyk NGinX configuration in place to handle domains.
However, I'd start off with targeting the API directly over the gateway on port 8080 and the APIID.