To use our native Wordpress integration you need to have the ability to install 'plugins' on your Wordpress website.
Although wordpress.com and wordpress.org is more or less the same thing, the .com version is super locked down and they wont allow you to install any plugin your want. The .org version is a little more fast and loose, you can modify your website however you like and instal any plugin you like, even plugins you make yourself.
The other requirement is that you have the correct access privileges to install plugins. If you don't see the 'Plugins' menu item in the left rail menu, you may not have sufficient access. To verify, go to 'Users -> all users' and look at the 'Role' column. You need to have 'Administrator' access to do this. If you only have 'Editor' access or something else, ask whoever setup your site to give you Administrator access or ask them to install the PushPress plugin for you.