Scaled resolution vs movie resolution on Mac Mini / 4k TV?

Anything showing on the screen will be 720p including movies. To see 4K you will have to set the resolution to 4K

You could try enabling HiDPI mode. In theory with a 'real' Retina display it should be possible to have the text and menus set to the equivalent of e.g. 720 resolution i.e. bigger, but still allow other software to take advantage of the full resolution to display pictures and movies. If you try doing this on a Mac mini which obviously does not have a retina display built-in then as standard it merely scales everything to the same level and does not enable this. If however you enable HiDPI mode then it might hopefully treat the display as if it was a Retina type display.

See http://www.eizoglobal.com/support/compatibility/dpi_scaling_settings_mac_os_x/

and http://www.fitzweekly.com/2016/03/enable-hidpi-resolutions-in-el-capitan.html

Holding down the Option key may also reveal some additional choices.

Before I tried enabling HiDPI mode but it only added options for low resolution for my 4K monitor

All the HiDPI modes will be quoting a resolution lower than 4K, the resolution they quote is the pseudo resolution for the Text and Menus, it should then be followed by the word 'HiDPI' as per the second link I provided. The HiDPI means programs able to take advantage of that mode should run in full resolution - apart of course from their text and menus.

See - Screen+Shot+2016-03-23+at+9.55.26+PM.png

If your not seeing any HiDPI choices listed then it is not working for you.

As always the only way to judge the success is in the eye of the beholder. So you would try a resolution e.g. 1080 or 720 without HiDPI in the entry, and then try one with HiDPI in the entry and view a photo and/or movie preferably paused to see if you can spot a difference.

That is what I saw in my display preferences. There is only HiDPI and the low resolution