quality_map = {'small': 0, 'medium': 1, 'high': 2}

def download_video(quality='medium'):
    k = quality_map.get(quality)
    print("Downloading {} -----------> {} in {} quality.".format(
        get_stream_map_list()[k], get_video_title_path(), quality))
    return urllib.request.urlretrieve(get_stream_map_list()[k], get_video_title_path())

while True:
    try:
        url, quality = input(
            "Please type a youtube video url and its quality(choose between high, medium and small) and separate them with a space: ").split()

    except ValueError:
        print("Please type the right url and quality.");
        print("Make sure the url start with 'https://www.youtube.com/'");
        print("high - for downloading high quality video");
        print("medium - for downloading medium quality video");
        print("small - for downloading small quality video");
        continue

    if validate_url(url) and quality in quality_map:
        get_sourcecode(url)
        download_video(quality)
        break

Then, I would move all of the main specific code into the __name__ == __main__ section because that's the purpose of that section.

#!/usr/bin/env python3.5.2

import urllib.request, urllib.parse
import os

def get_sourcecode(url):
    return urllib.request.urlopen(url).read()

def get_info():
    return urllib.parse.parse_qs(get_sourcecode(url).decode('unicode_escape'))

def get_video_title_path():
    try:
        return os.path.join(directory, '{}.mp4'.format(get_info()['title'][0]))
    except KeyError:
        print('Parsing error, please rerun the code!')

def get_stream_map_list():
    video_links = []
    for video_stream in get_info()['url']:
        if "googlevideo" == video_stream.split('/')[2].split('.')[1]:
            video_links.append(video_stream)
    return video_links

quality_map = {'small': 0, 'medium': 1, 'high': 2}

def download_video(quality='medium'):
    k = quality_map.get(quality)
    map_list = get_stream_map_list()[k]
    title_path = get_video_title_path() 

    print("Downloading {} -----------> {} in {} quality.".format(map_list, title_path, quality))
    return urllib.request.urlretrieve(map_list, title_path)


if __name__ == '__main__':
    print("\n                          * * * * * * * * * * * * * * *")
    print("                          *                           *") 
    print("                          * Youtube Video Downloader! *")
    print("                          *                           *")
    print("                          * * * * * * * * * * * * * * *\n")
    # make sure to change directory path
    directory = r'C:\Users\SalahGfx\Desktop\DownloadedVideos'

    while True:
        try:
            url, quality = input(
                "Please type a youtube video url and its quality(choose between high, medium and small) and separate them with a space: ").split()

        except ValueError:
            print("Please type the right url and quality.");
            print("Make sure the url start with 'https://www.youtube.com/'");
            print("high - for downloading high quality video");
            print("medium - for downloading medium quality video");
            print("small - for downloading small quality video");
            continue

        if url.startswith('https://www.youtube.com/') and quality in quality_map:
            get_sourcecode(url)
            download_video(quality)
            break