Going from Shimano 105 to Sram Rival - maybe.

I've just purchased a new road bike equipped with Shimano 105 components (compact double), but I had the chance to test ride a friends bike with Sram Rival and I LOVED the small hoods. I also liked how it shifted (double click was very intuitive for me).

If my goal is simply to get the smaller brifters on the sram, what other components do I also NEED to replace? I'm wishing to compare costs between upgrading the entire component set or just the bare minimum parts to get those smaller brifters.

You would need to replace the rear derailleur at a minimum. Not sure about the front. I would suggest speaking with the LBS that sold you the bike to see if they could work out something with you.