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The video card sends 8 bit per color data to the monitor.
 
The video player takes 10bit per color video and reduces the amount of colors using dithering until it's down to 8 bit per color and sends that to the monitor, at no point in time is the monitor seeing anything else than 8 bit per color.
 
10 bit encoded videos can have better quality because often, they're compressed using higher quality settings, or the bitrate (how much KB is downloaded for each second of video) is a bit higher.  So you get more quality from the start, and even if the player dithers it down to 8 bit per color, the video kept more of its quality all the way to you, compared to an equivalent 8 bit version.
 
Compressing to 10 bit per color can also help, because when compressing  video a lot of decisions are made about what's less important or more important to your eyes, what you notice or not when something moves in a scene (so that the encoder can reduce quality of picture where your eyes are unlikely to focus on and give more bits to areas you look at)... a lot of the math involved in making those decisions will have a few rounding errors when you're limited to 8 bits... so when you have 10 bits to work with yeah, you have more data to compress, but fewer rounding errors, the accuracy of the calculations often makes up for it, and you get more quality in the same amount of KB or just a few more KB required for same scene for better quality.
 
Cheap monitors are barely able to show the 8 bit per color, in fact a lot of them aren't even able to show those 16 million nuances of color ... nothing to worry about, play 10bit per color videos as much as you want, the video player will convert it down to 8 bit per color and play it like an 8 bit video.

if capable of throwing 10bit at a 8bit panel is fine..actually good. then the panel has plenty to work with when dispaying

Yes, it's always a good idea, it will have less banding and sometimes better contrast in subtle areas, but it's most likely unnoticeable in motion. It's a really subtle difference unlike playing UHD in 1080p where chroma upsampling is not required anymore (as 1080p Blu-rays have only 540p of color information).