PLT began takeoff on a 5200-ft dirt RWY (upslope to the south, elev 4775 ft) with wind from the south at 18-20 kts, density alt about 7250 ft. Witnesses observed the ACFT taking off, with the landing gear retracting as it passed their psn. Soon thereafter, the PLT transmitted he had 'a problem.' ACFT was then seen about 200-300 ft AGL in right turn, which progressed into a dive. ACFT impacted in flat attitude 1/2 mi south of RWY 17. PsgR video tapes revealed props went out of sync about 6 sec after takeoff. About 15 sec later, right prop slowed until blades could be seen turning. Video showed one ENG fuel flow at about 90 GPH, OTR ENG at min setting (abt 3 PSI), 5 deg increase in pitch attitude. Exam revealed RGT ENG driven fuel pump drive coupling was scored and only partially engaged. SB ME88 3 complied with; AUX fuel pump sws found in low psn. RGT prop blades fnd at fine pitch, lacking rotational dmg. LNDG gear fnd up, but unlocked; flaps extdd 15 deg. Emerg proc trng did not replicate hi density alt and max gross weight performance.