Reconciling power dissipation and output characteristic of BJT
My question is how these two seemingly contradicting characteristics
  can be reconciled.


It's all covered or implied in another curve called the safe area of operation and this curve factors in time or duration: -



So, for example, with a current of 1 amp and a collector emitter voltage of 10 volts the power dissipation is clearly 10 watts but this can't be indefinitely applied - notice how the curve above has time limits of 1 second and 10 ms shown. 

This is how the characteristic is produced in your question; voltage and current are applied for a short period of time. See the red boxes below: -




  I plan to use this transistor in an RF amplifier.


See the purple boxes above.

It's not a very good RF amplifier. \$F_T\$ is 200 MHz and that's the frequency where \$\beta\$ drops to unity. At 2 MHz, \$\beta\$ will be 100 but drop linearly to unity with frequency hence, at 10 MHz \$\beta\$ will be 20 and at 100 MHz \$\beta\$ will be 2 etc..

If your RF frequency is below about 5 MHz then it should be OK.

Be aware