Is it safe? Yeah, most of these models are. There are a variety of them using the same case with vastly different internals. There have been reported issues on some with swapped live/neutral or worse live/ground (at least then it doesn't power up so you KNOW something is wrong unless you touch the case

). Truth be told, almost all though are fine; the bigger issue is reliability. The quality isn't great, some have overheating issues (can only do 5A for a few minutes before shutting down), intermittent failures, etc. Also, these have really bad turn on overshoot. Meaning when the power is turned on, the rail spikes up to dozens of volts and then settles back down. This isn't a safety issue but it CAN kill your projects if you have everything plugged in before you turn it on. Very frustrating for a first time learner who isn't expecting it.
Could it burn down your house? I could burn down your house with a nine volt battery and some steel wool.

The voltages and amperages on these are acceptable for his age. The amperage is a bit higher than he needs, but nothing I would worry about in the least bit. If he's asking for one of these, he likely knows what he is doing. By the way, send him over to EEVBlog, its like this forum but for electronics, circuit design and test equipment. Nanofrog and I hang out over there as well (then again, maybe thats more a reason to keep him away).
If I might step-in and offer some advice for you and him. I'd go for something a bit older and with at least TWO isolated channels. The two isolated channels allows for the supply to function as a +/- supply which is essential for learning electronics topics like OP-Amps and amplifiers. The older models won't have the digital displays at this price point, but the cheap ones are seldom that accurate anyways. That being said, like old tools, the quality is dramatically better and the value CAN be significant. My
favorite single channel bench supply cost me $100, it is a specialized high precision supply. To match that performance in a modern new instrument I would be looking at close to $5000. Though, it can take time sorting through the people who have a turd and think they have a goldmine to find the real deals there are great deals out there. For what I mentioned, you might pay a bit more than the cost of the supply you linked but the quality would be night and day better. It depends on how much searching you do (craigslist and local university surplus are GREAT locations to find these things for pennies on the dollar) and how much time you have. Some times, there are almost no deals to be found and other times there are dozens of them.
At the end of the day, you know your budget and your son. The supply he linked should do OK, there just might be better options if you expands things a bit. If you have any questions feel free to ask.