1. DisplayPort to HDMI adapters are for connecting DP computers to HDMI displays. They won't work the other way around.
2. G-Sync only works on DisplayPort, it won't work through an adapter of any kind, unless it's from DisplayPort to Mini DisplayPort or vice versa.
3. I doubt your GTX 1070 has only HDMI and no DP. DP and HDMI look very similar. Check again.