To add to this, gaming is never something that remote connections do very well. The VNC protocol in use by the eMac isn't very efficient to begin with, and the eMac basically can't even begin to be powerful enough to do the decompression on a more powerful protocol, in the way, say, an nVidia SHEILD tablet can.
The one possible saving grace would have been if the eMac had gigabit Ethernet, but it seems that even the 1.42GHz model only has 10/100. It looks like the earliest small Mac with gigabit is the
1.8GHz 17-inch iMac G5. You
might have better luck with that system, but unfortunately, VNC is just a very inefficient protocol, because essentially what it's doing is sending a series of full-screen, full-color, (usually) uncompressed screenshots over the wire, and that takes hecka network throughput.
There's a good reason that, even with thin client hardware becoming as powerful as it is, nobody considers them to be good at tasks such as gaming or CAD and 3d work.