Most intel CPUs and some Ryzen CPUs (the APUs to be precise) have an iGPU in them.
No modern consumer motherboard has a GPU.
You also seem to think that laptops have CPU sockets and not soldered on processors which is also just wrong
You said that intel advertises that the i3 line is designed for mobile devices (I assume you mean laptops because to my knowledge no mobile device uses an intel CPU) but that also isn't true.
https://www.notebookcheck.net/Intel-....446651.0.html
Look at this article specifically this part
"On one particular slide, they claimed that the i3 9350K was faster than the entire Ryzen 5 3xxx product stack at gaming, office work, content creation, and other uses."
Clearly intel thinks i3s are designed for gaming.