Example using Ansible API 2.0 to run a playbook

ansible_api_playbook.py

#!/usr/bin/env python
# stolen from http://stackoverflow.com/questions/27590039/running-ansible-playbook-using-python-api

import os
import sys
from collections import namedtuple

from ansible.parsing.dataloader import DataLoader
from ansible.vars import VariableManager
from ansible.inventory import Inventory
from ansible.executor.playbook_executor import PlaybookExecutor

variable_manager = VariableManager()
loader = DataLoader()

inventory = Inventory(loader=loader, variable_manager=variable_manager,  host_list='/tmp/hosts')
playbook_path = '/tmp/ls.yml'

if not os.path.exists(playbook_path):
    print '[INFO] The playbook does not exist'
    sys.exit()

Options = namedtuple('Options', ['listtags', 'listtasks', 'listhosts', 'syntax', 'connection','module_path', 'forks', 'remote_user', 'private_key_file', 'ssh_common_args', 'ssh_extra_args', 'sftp_extra_args', 'scp_extra_args', 'become', 'become_method', 'become_user', 'verbosity', 'check'])

options = Options(listtags=False, listtasks=False, listhosts=False, syntax=False, connection='local', module_path=None, forks=100, remote_user='stephen', private_key_file=None, ssh_common_args=None, ssh_extra_args=None, sftp_extra_args=None, scp_extra_args=None, become=False, become_method=None, become_user='root', verbosity=None, check=False)

variable_manager.extra_vars = {'hosts': 'localhost'} # This can accomodate various other command line arguments.`

passwords = {}

pbex = PlaybookExecutor(playbooks=[playbook_path], inventory=inventory, variable_manager=variable_manager, loader=loader, options=options, passwords=passwords)

results = pbex.run()

wonderful！

Does this actually work for you? I'm seeing:
./test2.py
Traceback (most recent call last):
File "./test2.py", line 10, in
from ansible.inventory import Inventory
ImportError: cannot import name Inventory

No it does not, the API has changed.
Look at this document https://docs.ansible.com/ansible/latest/dev_guide/developing_api.html