You don't have to have an install.php file as part of your plugin. You do need to have install.xml for an activity to create the main activity table and any additional tables you might need for your plugin.
install.php is used if you have any processes or data perhaps that need to be added at install time. I've had a quick glance through the default mod plugins that ship with Moodle, and only 2 have anything in install.php beyond a placeholder function. mod_lti and mod_survey. mod_lti checks that some key has been defined somewhere else, and mod_survey loads up its tables with some data.
If you do need to use install.php, you create a function named: xmldb_yourpluginname_install().
Of more use is the upgrade.php file. So it's well worth having a dig around existing plugins to see what they're doing there.