If your son wants to make HD (high definition) recordings of game plays, then
Hauppage HD PVR is a good choice.
AverTV HD DVR can also make HD recordings, but unlike HD PVR it uses the resources of your computer to encode videos, so your computer must be powerful enough (this process is very resource intensive). And it requires your computer to have a PCI-E slot (so if you have a desktop, not a laptop).
If SD videos are good enough for your son, then
EasyCap can be used. It doesn't offer great quality, but it is very very cheap.
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