How can I properly tell if a wall wart is OK to use for old hardware?
The rating on the wall wart for current is the maximum it can supply at the rated voltage output usually. What your Sega takes from that wall wart is a totally different matter so, when you concluded that: -


  it appears the model 1 needs 1.2A/9V DC


You may have been misguided.

The best way to determine what current is needed by your equipment is to contact the original supplier but this may not be appropriate due to the data being unavailable on olde products like the Sega thing. Measuring it yourself can appear easy but, are you measuring current taken when device is working the hardest?