Combining other answers, here is a short solution without overloading Loader class and it works with any loader operating on files:
import json
from pathlib import Path
from typing import Any
import yaml
def yaml_include_constructor(loader: yaml.BaseLoader, node: yaml.Node) -> Any:
    """Include file referenced with !include node"""
    # noinspection PyTypeChecker
    fp = Path(loader.name).parent.joinpath(loader.construct_scalar(node)).resolve()
    fe = fp.suffix.lstrip(".")
    with open(fp, 'r') as f:
        if fe in ("yaml", "yml"):
            return yaml.load(f, type(loader))
        elif fe in ("json", "jsn"):
            return json.load(f)
        else:
            return f.read()
def main():
    loader = yaml.SafeLoader  # Works with any loader
    loader.add_constructor("!include", yaml_include_constructor)
    with open(...) as f:
        yml = yaml.load(f, loader)
# noinspection PyTypeChecker is there to prevent PEP-check warning Expected type 'ScalarNode', got 'Node' instead when passing node: yaml.Node to loader.construct_scalar().
This solution fails if yaml.load input stream is not file stream, as loader.name does not contain the path in that case:
class Reader(object):
    ...
    def __init__(self, stream):
        ...
        if isinstance(stream, str):
            self.name = "<unicode string>"
            ...
        elif isinstance(stream, bytes):
            self.name = "<byte string>"
            ...
        else:
            self.name = getattr(stream, 'name', "<file>")
            ...
In my use case, I know that only YAML files will be included, so the solution can be simplified further:
def yaml_include_constructor(loader: yaml.Loader, node: yaml.Node) -> Any:
    """Include YAML file referenced with !include node"""
    with open(Path(loader.name).parent.joinpath(loader.construct_yaml_str(node)).resolve(), 'r') as f:
        return yaml.load(f, type(loader))
Loader = yaml.SafeLoader  # Works with any loader
Loader.add_constructor("!include", yaml_include_constructor)
def main():
    with open(...) as f:
        yml = yaml.load(f, Loader=Loader)
or even one-liner using lambda:
Loader = yaml.SafeLoader  # Works with any loader
Loader.add_constructor("!include",
                       lambda l, n: yaml.load(Path(l.name).parent.joinpath(l.construct_scalar(n)).read_text(), type(l)))