So if you take your company laptop home, connect to the VPN, and then try to launch the software from your laptop....what happens?

You are using the VPN to access your company network, so if your laptop works in the office it should work over the VPN. I'd guess the RDP step is meant for people using non-company machines without the software installed.

There are possible exceptions. The remote software might only allow incoming connections from certain IP addresses, and the VPN might not connect you to one of those.

We had a silly situation at work in which only certain machines could punch in and punch out for shifts, but you could always use the VPN to do it. If I was finishing my shift in someone's office and didn't want to circle back to my department, I could connect to my phone's hotspot, VPN into the company network, and punch out.

I'm a firm believer that if you don't want me to do something, I shouldn't have access to do it. I'm not a malicious person though, just efficient.