OK, on IRC, fundies helped me out a bit. Here's a log of the conversation:
<onpon4__> Does anyone here use Ubuntu LTS, by any chance?
<fundies> we have few ubuntu users here but not lts
<fundies> onpon4__, you have enigma issue? or ubuntu issue?
<onpon4__> fundies: http://enigma-dev.org/forums/index.php?topic=1631.msg15755
I just wondered if I could easily weed out this problem being with Ubuntu LTS.
<fundies> can you compile empty game?
<onpon4__> fundies: Nope.
<-- theweirdn8 (6cfcb122@gateway/web/freenode/ip.188.8.131.52) has left #enigma
<DarkAceLaptop> ur hysterical fundies
<fundies> onpon4__, paste me a full log of empty gaym
<DarkAceLaptop> he means game
<onpon4__> fundies: Just up to the error, right?
<fundies> onpon4__, log from the terminal not lgm's console
<onpon4__> fundies: Everything, including what's printed between the error happening and LGM being closed?
<fundies> java -jar lateralgm.jar &> log.txt
after lgm opens hit run
<onpon4__> Alrighty then.
<fundies> once it fails close it n gimme log.txt
<onpon4__> fundies: Here you go: http://pastebin.com/gz8r3xF3
<fundies> DarkAceLaptop, nah its gaym
<DarkAceLaptop> fundies is still learning how to spell, you see
<fundies> onpon4__, in another terminal inside the enigma-dev directory
<fundies> make Game GMODE=Run GRAPHICS=OpenGL1 AUDIO=OpenAL COLLISION=Precise WIDGETS=None NETWORKING=None PLATFORM=xlib CXX=g++ CC=gcc COMPILEPATH=Linux/Linux EXTENSIONS=" Universal_System/Extensions/Alarms Universal_System/Extensions/Timelines Universal_System/Extensions/Paths Universal_System/Extensions/MotionPlanning Universal_System/Extensions/DateTime Universal_System/Extensions/ParticleSystems Universal_System/Extensions/DataStructures" OUTPUTNAME="/tm
DarkAceLaptop, shush ur ass
<onpon4__> fundies: I get an error with that as well.
<fundies> paste it please
<onpon4__> fundies: http://pastebin.com/GAcqp99p
that errors cause noones merged https://github.com/enigma-dev/enigma-dev/pull/528 yet
though im not sure wht lgm is having trouble running make
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After I switched to fundies' fork on GitHub, I was able to compile a blank game, the FPS example, and the isometric Mario example. The platformer thing still doesn't work, and I still have the same crash with Bowser's Last Stand, so the problem's not solved, but it's a step forward, anyway.
EDIT: The rest was a corrupt GMK, as was found out on IRC.