The integrated graphics on newer processors are better than the high-end GPUs a decade ago. They're certainly powerful enough to for Minecraft. The benchmarks I'm seeing say that the integrated graphics in this processor can hit 50-60 fps in Minecraft at 1080p.
The biggest drawback of all-in-ones is that they combine the monitor with the computer. A computer is typically obsolete after 5-7 years. A monitor will usually last 15-20 years. So you're needlessly investing your money in something (a monitor) that you'll be forced to throw away while it still has 2/3 to 3/4 of its usable life left.
Personally I'd go for a laptop. The anywhere capability of portable computing cannot be reproduced by a desktop, and the larger screen of a laptop provides something a phone or tablet cannot. If you wish to use it as a desktop, you can always buy an external monitor, mouse, and keyboard. The only drawbacks are expense (both purchase and repair) and (lack of) upgradeability. But streamed gaming is getting to the point where you can run a game on a powerful desktop PC, and stream it to a laptop or tablet for hours of gaming on battery away from the noise and heat. You only really need to play on the desktop if you're a hardcore gamer who wants 144 fps with G-sync.
If you think your daughter will stay interested in 3D gaming, a desktop would let you upgrade the GPU in the future. It's just that at the age most kids are interested in Minecraft, it's impossible to say what their future interests will be. So the upgradeability of a desktop *might* be useful, whereas the portability of a laptop *will* be useful (unless your kid already has a tablet).
This may just be a personal preference, but I'm not a huge fan of all-in-ones. I much prefer a conventional tower. There are a number of reasons for this: all-in-ones are generally overpriced, it can be difficult to upgrade components in the future and if the monitor malfunctions you have to pay for a screen replacement.
I'm not going to say it's a terrible PC for the price. It's decent, although you can likely find better systems for less. This system is geared more towards the average user than any form of gaming experience.
The biggest thing that would turn me off is that this system (and typically all-in-ones in general) lack a graphics card. A graphics card is something that's highly recommended for any gaming. It's also important to think about the future. Sure, your daughter likes Minecraft now, but there's no telling what games she will want to play in the future. As time progresses, a graphics card is becoming increasingly important.
Is this one better ? I like the bigger screen...
This one does seem to be higher quality. The biggest difference is that it has an Intel processor instead of an AMD and NVIDIA instead of AMD for graphics. And then of course the bigger screen as a plus.
There are some drawbacks with this one though. Walmart is, generally, not as helpful with technical support (should you require any) compared to Best Buy, given that Best Buy is a technology store.
Also, and keep in mind this is based off of my own experience, I've not had much luck with Dell in the past. They are a highly regarded electronics manufacturer, but I've had issues with technical support and warranty hassles with them in the past. That's not to say that you will have the same experience, but I just figured I'd share that. I'm sure there are people with similar stories about Acer, so take my experience with a grain of salt.