Note of Warning...
I found this online and there are no updates for it. It is based on the Older Minecraft 1.25 and 1.52 series for the G4 and G5 systems respectfully. Currently Minecraft is at 1.8x at the time of this writing.
 
I have had tried to get Minecraft to run on the Mac G4 back in 2017/2018 but it failed due to various errors in the Java itself and Apple has ended Java support for the PowerPC Macs as far back as 2010. Furthering this, Oracle ended Java Support for the PowerPC Systems (Apple, IBM, etc.) back in 2015. Thus getting a newer version of Minecraft to run on the older G4 and G5 systems is a near impossibility.
 
But thanks to various individuals out on the internet, they have compiled a version of Minecraft for the older G4 and G5 systems, and can access older personal server that are still on the ‘net. It still needs Java for most things but those modules that can be complied were to take advantage of the hardware, including 3D acceleration the older nVida had with OpenGL. This is hilarious because the Older PowerPC systems had the better video card in them than their “modern” Intel systems which used the Intel 950x Video Cards that did not support OpenGL.
 
Another word of warning is the playability of the game. Despite that the G4 and G5 are going to be slow (to be explained later), the main issue is with the control of the game. The Macintosh system since its inception has always ran with one (1) Mouse button, and the game having ran on PCs through Windows and Linux uses two (2) to three (3) mouse buttons. Thus one is either have to change the key options on the game, get a 2 or 3 button mouse for the Mac or get one of those rare game controllers that will work on a Mac.
 
How To Do It...
 
In all honestly, I forgot and lost the link where I got the files but I am posting the compressed files on this system. Minecraft 1.25 is for the G4 system and Minecraft 1.52 is for the G5. You need a minimum of a 800MHz CPU with 1GB of RAM and OSX 10.3.8
 
The instructions are simple. 1) Copy the compressed file to the Desktop. 2) Decompress the file, it will create a folder with 4 files in it. 3) Open folder and double click the “Installer” file. This will install Minecraft to your Application folder and the Java Extensions into Applications Support folder of your account’s System Library folder. During the install it will ask for your or the System administrator’s password in the terminal window. Then it will complete the installation process.
 
How To Play
 
I’m not saying how to play the game as the rules of Minecraft is simple. Keyboard control is standard, but the issue is with the Mouse control as stated above. To install a block, hold the “Control” Key and click the mouse button if you are using a standard Mac Mouse.  
 
You have the standard get of game settings, application settings and other settings to control like normal. You can also play on various independent servers that will allow your version to log in. Current (Microsoft) Servers will not allow you to log on with the older version you are running. But there are many independent servers running various servers like CraftBukkit and Spigot.
 
Cavet Emptor
 
Buyer Beware...?
 
Though the minimum to run these versions of Minecraft is a CPU running at 800MHz with 1GB of RAM, the minimum is not the best to run the game on. I ran the G4 version on two (2) separate systems that I have: a Mac Mini G4 with a 1GHz CPU and 1GB of RAM running OSX 10.4.11 and a Powerbook G4 with a 15in screen with 1.5GHz CPU and 1.5GB of RAM.
 
Running Minecraft on the Mac Mini was slow. It took a long time for the world of the game to be built, and it is slow on the controls. I remember reading somewhere that the game should operate on at 20 to 30 frames per second (fps) on the minimum set up. This is not so, as playing the game on the Mac Mini shows it to run at 15fps or slower and lagged on field updates.
 
Running Minecraft on the Mac Powerbook resulted in better results. With more RAM and a faster CPU, it was able to play much smoother and faster. Field updates stalled for less than a second but hardly noticeable. Animation was nominal, smooth and flowing.  Controls were smooth and responsive.
 
The questions lie in besides the RAM and CPU, was the hard drive also a hindrance to running the game? I will have to invest in getting a SSD in PATA Format to test this idea with the Mac Mini. Also, the G4 Mac Mini Maximum RAM is 1GB though the CPU can be boosted to 1.25GHz with a hack. These options I will have to investigate.
 
I have not tested Minecraft (either version of 1.25 or 1.52) on my G5 system. I will have to get it out of storage, set it up and install it. But it looks promising for it to be the best vintage system to run Minecraft on. From the findings I have, any G4 system better than 1GHz with more than 1.5GB of RAM would be good to play on. I do have a couple other G4 Systems to test Minecraft on but that will also be in the future.
 
Until then, Happy Crafting.
 
Links:
For G4 Systems - http://www.hondosackett.com/yabb/VintageComputers/Minecraft_1.2.5_Definitive_G4_ 5.zip
For G5 Systems - http://www.hondosackett.com/yabb/VintageComputers/Minecraft_1.5.2_Definitive_G5_ 0.zip