The prior answers to this question were written as early as 2015, before Raspbian's introduction of the open-source driver.
On a Pi 2 or higher, run:
and enable the OpenGL desktop (Mesa) driver under Advanced Options -> GL Driver. Note that on a Pi 4, OpenGL with Fake KMS is already the default configuration.
When the Legacy driver has been disabled, the helper script at
/usr/bin/minecraft selects Mesa via an injected library in
ssh -X then works as expected to play Minecraft Pi Edition remotely. Moreover, this achieves higher remote framerates compared to RealVNC's experimental direct capture mode.
Despite comments saying the contrary, use of
ssh -X does not require an X session to be running on the Pi server. A session is needed only on the client which may be a Linux x86 or even Windows PC, another advantage over VNC.