Genuinely confused - which other people? There are no other people with your Gmail address but added/removed '.' characters. What you're seeing is people sending emails to the wrong email address - nothing to do with presence or absence of '.' characters.
Allowing addresses to subtly differ based on '.' presence/absence would result in more wrongly addressed emails, hence the aliasing.
I've been getting wrong Gmail emails all the time for years because a woman in Saskatchewan keeps getting her email wrong when signing up to stuff online. Quite funny really but nothing to do with .'s