Remember I'm running WildFly remotely, bound to 192.168.59.103 as IP. WildFly is already up and running.

Open a new terminal window and execute the following commands:

$ cd $WILDFLY_HOME
$ ./bin/jboss-cli.sh -c --controller=192.168.59.103:9990 --user=wildfly --password=cookbook.2015 --command=":read-attribute(name=launch-type)"
{
    "outcome" => "success",
    "result" => "STANDALONE"
}

Obviously, you can extract just the information you need using the awk command in the output (you can use whichever tool you are comfortable with), as follows:

$ ./bin/jboss-cli.sh -c --controller=192.168.59.103:9990 --user=wildfly --password=cookbook.2015 --command=":read-attribute(name=launch-type)" | awk 'NR==3 { print $3 }'
"STANDALONE"

In case you are running WildFly in the domain mode, the invocation is the same, but...