I didn't have an issue with installing DirectPlay when requested upon starting Rollercoaster Tycoon. If the add remove features isn't working for you, though, you could try the command line method:
dism /Online /enable-feature /FeatureName:"DirectPlay" /NoRestart
Or if that doesn't work you could try and perform it via a Windows 10 install USB and instead of /Online you use /image: i.e. dism /image:C:\ /enable-feature /FeatureName:"DirectPlay" and reboot back into the OS. I've not installed DirectPlay to an offline image but have done .NET 3.5 "netFX" via dism without an issue so see why DP should work.