Venmo is like Paypal or any other payment app. She has one dollar to her name and he asks for her Venmo id, she thinks he's going to give her money to help but instead he sent a request to her account asking her to give him the one dollar.
Venmo is an app used to send cash with a little note to describe what it's for. It's owned by PayPal. When someone asks for someone else's Venmo, it normally means they want to send cash. The person with $1 remaining must have given their Venmo info out hoping to get some help, but instead the person who asked for it requested their last dollar.
That's an explanation of what is happening here. I can't tell you why it's funny as requested, but that's because it's really not that funny
I can explain why it's funny: Most expect the person to send money and help, instead he is asking to take the last dollar. Comedy is, at its core, a subversion of expectations. This is an example of that idea.