The LG27UD88 monitor is indeed a piece of confusing engineering. You have too many options.
If your videocard does not have the Type-C output and you are using DisplayPort, the DP link does not have the USB capability. The Type-A USB3.1 receptacles will not work unless you connect the LG Type-C port via additional C-C cable (to Type-C host) or C-A cable to a regular USB-A host port.
You can connect the monitor via Type-C port to a Type-C host (using C-C cable), if the host supports Display Port video over Type-C. But then you will need a very special support from host to have USB functionality, because the cable can do either USB, or DP @ 4K resolution,[see correction/clarification below].
You can use HDMI ports, then #(1) still apply.
The monitor also has tremendous number of options to charge smartphones, but I was lost there.
Enjoy your nice 4K monitor.
TECHNICAL CLARIFICATION: Thanks to comment by Alexander Kosubek, a full-featured C-C connection can support both USB3 (taking two diff-pairs in the cable) and a two-lane DP. However, to support 4K display resolution, the DP must be revision 1.3, while the LG27UD88 can do only v1.2. More, both display and PC host must support a "Type-C alternative mode" as "USB DisplayPort Dock", which implies full support for Power Delivery function, which is needed for proper discovery of Type-C partner. In all cases the USB2 link is supposed to be functional, although it is unclear how it is used in the display. If this makes the use of LG display any less confusing, then this is it.