According to benchmarks, the Geforce 9500 GT is close to the Intel HD 4000 listed in the requrements, some saying the 9500 GT is slower. The Radeon HD 7750 and Upsydaisy's Nvidia GTX 950 are both significantly faster, with the GTX 950 being the fastest.
I don't have all of Upsydaisy's specs, but Haven Moon was
***made with the Unity game engine***. According to
***this***, Unity announced they were adding VRWorks support earlier this year, which would give a performance advantage to newer Nvidia cards. Maybe the Nvidia GTX 950 is able to do some things in hardware that take load off the processor, making the i3 adequate when using the GTX 950 while the i3 is not adequate when using other non-Nvidia and older low-end Nvidia cards. (
the 9500gt is from 2008 while the
GTX 950 is from 2015.)
That would be my guess as to why Upsydaisy's computer is playing the game OK despite using an i3 -- that the GTX 950 is taking some of the workload off of the i3.
Another possibility may be antivirus scanning the game and using up processor cycles. Try to add the game's exe to the antivirus' exceptions list so it won't be trying to scan the game while you're playing. If you want to try disabling antivirus entirely, be sure to disconnect from Internet first.