Nearly all laptops with dual graphics (e.g. Nvidia Optimus) use both GPUs. The Intel integrated GPU is always on and always drives the screen. The Nvidia GPU acts as a co-processor. The game renders each frame on the Nvidia GPU, then the Optimus drivers transmit the completed frame to the Intel GPU. The Intel GPU displays it on the screen. It's like you have v-sync always on, with the two GPUs acting as the two v-sync framebuffers.
A few gaming laptops are set up so the Intel GPU drives the laptop screen, while the Nvidia laptop drives the external monitor port. And a few are set up with a BIOS option to let you disable the Intel GPU completely and have the Nvidia GPU drive the screen. But the vast majority of laptops including all non-gaming laptops I've heard of leave the Intel GPU in control of all displaying.
Since all the Intel GPU is doing when you use the Nvidia GPU is copying and displaying the frames it receives, the spike in the Intel GPU's usage would suggest a bug or conflict in your display drivers. The Nvidia's framerate is probably dropping because it's waiting for the Intel GPU to clear up the problem. Try downloading the Intel and Nvidia drivers from your HP's website, then turn off WiFi and unplug the ethernet cable and try the game again. If the problem disappears, re-enable the network connection.
If the problem comes back, then Windows is replacing your functioning Intel/Nvidia drivers with broken ones because it thinks they're newer and better. That usually works fine with desktop computers with a single GPU. But Optimus requires the two drivers and the Optimus driver to work closely together. Go to device manager (Windows key + x), and righ-click the two GPUs to open their properties dialog. Go to the drivers tab, and roll back to the previous driver if it's different from the one you installed. That should prevent Windows from updating over your working drivers again.
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