I am unsure if this is old news or not and some of the ASM programmers probably alerady expected or discovered it, but it seems that PindurTI, which is a TI-82, TI-83 and TI-83+ emulator, supports the TI-73 as well. Altough the support wasn't intentionally built-in (if you try to send TI-73 files to the emulator you will get an "Invalid File Type" error), I tried to nagivate through menus and test some stuff and everything seemed fine, as you can see in the two following screenshots:

According to many sources, such as old topics on United-TI forums and http://www.datamath.org website, the TI-73 hardware is practically identical to the TI-83+ and the only difference is the software loaded in the Flash memory. As some people alerady tried to load a TI-73 OS on a real TI-83+ before, this makes me wonder if the emulator isn't recognizing the TI-73 ROM I sent to it as a TI-83+ one? Altough this is not much of a discovery, I found this a bit interesting since the emulator wasn't even meant to have support for this calculator model.

WabbitEmu old version from 2007 had built-in TI-73 support, as stated on Revsoft forums. As proof I got able to send such files to the emulator run Joltima with Mallard shell in it fine:

This makes me wonder why the exact same ROM would not even load at all in the newest version of WabbitEmu until you restart the emulator completly, though. Also the same experiment than with PindurTI didn't worked with VirtualTI 2.5 beta.

I only tested this with ROM version 1.40, though. I haven't tried with 1.3004, 1.3007, 1.60, 1.90 or 1.91. Also I haven't personally tried doing such thing on a real TI-83 Plus calculator nor even loading a TI-83+ OS in a TI-73 so if you ever plan to do so it is at your own risks.

Actually the reason why we need to send an hacked backup file to the calc to be able to run ASM is because the TI-73 OS, not the calc itself, has no command to run ASM. The first calc to have built in ASM command was the TI-83 and it was still not a real command. Instead of Asm(prgmNAME it was Send(9prgmNAME (the "9" is not a typo). I'm sure even the TI-81 could have run ASM games if it had a link port. The only thing is that the TI-81 z80 is at 2 MHz so games would be 3 times slower. The TI-80 is out of the question because of the different processor it uses.

Nah it doesn't have a link port either

Joltima is a 1998 RPG that got released on the TI-83 then ported on TI-82, 85 and 86 in 1998-1999 and on TI-83+ in 2001. Later in 2005 I think it got ported on the TI-73 after people discovered how to hack the 73 to run ASM games in non APPS form on it. It's considered as one of the best RPG for TI calcs despite the lack of magic spells in battles making them repetitive and the game being a bit too easy

Back then there was a Gameboy Color homebrew game Joltima 2 in the works but it never got finished. Not even a demo came out.

http://www.ticalc.org/archives/news/articles/1/19/19184.html

The game was later renamed to Infinity then cancelled in 2002