Thought I'd mention, GT1030 doesn't support HW Encoding, could this be your issue?
GPU is decoding your media correctly, as I can see it's been used in GPU Statistics - it's then your CPU which is encoding the media, which I'm assuming is H264. From the screenshot I can see you have a dual core CPU, this isn't gonna like software encoding unless the encoding profile is set to 'veryfast' and extremely low resolution, and also a extremely low bit rate.
Also, when anything is transcoded, the audio part of transcoding is handled by CPU
So at this time, your dual core CPU is encoding audio and video, while your GPU is doing the decoding. It's got it's work cut out, would possibility explain the stuttering