There are few wrong assumptions and they led you to wrong conclusions:
Many motherboards marketed as "gaming" has an integrated Intel graphic
The graphic card is on CPU. Intel made this decision, not motherboard maker. When buying Intel, GPU cannot be avoided.
I understand that putting in an integrated graphics into a motherboard
increases it's cost.
It depends on what you're looking at. If you look at price of chips alone, the costs are not ground breaking. On LGA775 platform the GPU was integrated in chipsets, so some had integrated GPU while others were genuinely lacking the processing power. However, the low-end chipsets with GPU (eg. G41) were actually cheaper than high-end chipsets without GPU (eg P45). So we can conclude that while integrated card must increase the price of a chip, it's not really enough to justify costs of making 2 lines of chips: with and without. This is probably why Intel decided to put a GPU on every single consumer CPU.
Now, since the GPU is already on the silicon, we can consider the costs that can be decided by motherboard designer. If he wants to make the GPU work, he adds the connectors (probably the most expensive part of implementing onboard GPU this days), traces, and a handful of dirt-cheap passive components like those tiny resistors and capacitors. Those costs are still negligible. If we were talking about lowest-end budget motherboard, axing few dollars would probably be at least put under serious consideration - but on a high end motherboard that is already expensive any possible savings are negligible.
This is because integrated video do not have a chance to compare with
higher end Nvidia/Radeon offerings.
I cannot really call you wrong on this one. With high-end they can't compare. However, the old wives tale that integrated GPUs are useless isn't true anymore! There are 2 desktop Intel processors (LGA1150 Broadwell, Core i5-5675C and Core i7-5775C) that have integrated Iris Pro Graphics 6200 that was a shock when it was released in Q2 2015. It's performance is comparable to low end discrete GPU, so it can be actually used to play most games on lower detail. If you're a gamer on tight power or space budget (eg. console-sized living room PC), I believe this would be a way to go. This integrated GPU was probably quite expensive, that's why it's seen only on $276 CPU.
There is also an elephant in the room here. I believe you've assumed that "gaming" means "top performance". Well, it does not. It's simply a marketing strategy. Nobody is really able to tell what "gaming" label means, except that it features aggressive styling and a higher price tag. Basically a premium product. So, when in doubt, just add every feature you can and you'll have one more point on feature list. Like pretty RGB lights that most users will probably lock up in the case and shove under the desk to be never seen again or shiny metal over PCI slot that does nothing but looks cool. (Seriously, lights? How are they in ANY way useful in gaming? I can't believe you questioned integrated GPU while there are lights on the mobo!)