Today RGB lighting systems come in two dominant versions, although there are a few others. The plain RGB system uses a 4-pin header that supplies a common +12 VDC line plus three different Ground lines, one for each of the three LED colours (Red, Green, Blue). The more complex Addressible RGB or ADDR RGB or ARGB system uses a 3-pin header (looks like the 4-pin one with one pin missing) that supplies common +5 VDC and Ground lines, and a digital Control Line. The last line carries addressed data packets to the individual node control chips along the light strip. So these two are NOT compatible, and there is no good way to convert one to the other with a simple adapter.
The system you got for your nephew is the ARGB lighting type and has two options. You can simply use the included remote control to set lighting display patterns manually. IF your mobo has a 3-pin ARGB header, you can connect a cable from that to the fans' control box and let that signal drive the fan lights. BUT you believe there is no 3-pin header on his mobo, so you cannot do that at all.
If you want to be sure, get the maker and exact model number of your nephew's mobo and post here so we can look it up. Mobos are sold these days with no lighting headers, with only plain (4-pin) RGB headers, with only ARGB headers, or with both types of headers. What you get depends on which mobo you buy. The mobo maker's NAME for their lighting control utility software does not tell you which type of hardware lighting system they have included in a mobo.