Will it run

Solution
Yes, it is better. But why do you want an all-in-one PC? They are basically like laptops in the sense there is very limited upgrade options. You cannot upgrade the CPU or the graphics. Once the graphics capability no longer meets your expectation, then there is nothing you can do other than live with it or buy a new PC.

While the Intel HD 4400 graphics core is better than the Radeon R5 graphics core, it is still weak compared to an inexpensive graphics card.
It will run Minecraft, but not at 60FPS; even if you use the Optifine Mod.

The A8-7410's Radeon R5 (Carrizo) integrated graphics core is not much faster than an Intel HD 4000 graphics core found in 3rd generation Ivy Bridge Intel CPUs.

I have read that the Windows 10 version of Minecraft has a little better performance compared to the older versions of the game, but mods created for the older versions (like Optifine) are not compatible with the Windows 10 version of Minecraft.

You can search Youtube for the phrase Minecraft Intel HD 4000 to get an idea of the A8-7410's performance in that game. Naturally, you should look for video showing the game being played at 1080p if that is the resolution you want to play at.
 
Yes, it is better. But why do you want an all-in-one PC? They are basically like laptops in the sense there is very limited upgrade options. You cannot upgrade the CPU or the graphics. Once the graphics capability no longer meets your expectation, then there is nothing you can do other than live with it or buy a new PC.

While the Intel HD 4400 graphics core is better than the Radeon R5 graphics core, it is still weak compared to an inexpensive graphics card.
 
Solution