Running Alpha Ship on a modded console offers several advantages:

Alpha Ship is a reminder of a wilder time in gaming history when anyone with a copy of XNA Game Studio could put their dream on your TV. On a JTAG/RGH system, it’s a snappy, addictive distraction that proves the 360’s homebrew scene is still very much alive.

While there isn't a widely recognized title explicitly named "Alpha Ship" in the mainstream Xbox Live Indie Games (XBLIG) catalog, the phrase likely refers to a specialized homebrew project or an early-access "alpha" build of a space shooter designed for modded consoles.