Before searching or installing anything always need to update the repo first
sudo apt-get update
An then install or search what you need.
Normally I always install synaptic
sudo apt-get install synaptic
Then you should have an icon in application launcher to run it, but if you type synaptic in the terminal I think it should work too.
Synaptic allow you to search for packages more easily. Just type libcurl or whatever package is missing by AppGameKit in the search box and it should give you a list of packages with description what each package is and you can select any package to install. Synaptic then going to configure dependencies and remove anything my conflict with the package you are about to install.
You can also search the package names online to find what you need for example it shows for libcurl.so.4 you need to instal the package libcurl3
If installing libcurl3 does not solve your problem then probably one more package is missing, I believe I had to install 3 packages to get AppGameKit working on a fresh install of Ubuntu 18.04 but can't remember what it was, if you run it from terminal it should always tell you what package is missing "not found".
I think it would be nice if TGC would include a shell script or something that we can run and it would go through all the dependencies required by AppGameKit IDE and AppGameKit Player and install them from the repo.
Or even better if we would get a snap package