I think an historical look at that competition helps make the fact that each engine played on its own distinct hardware setup seem more reasonable. Don't think of it as merely an engine (software) competition, because it wasn't. Instead, think of it as a competition to determine the strongest chess-playing machine (hardware and software combined). And really this isn't so strange, especially given that this series of events dates back to an era when engines themselves were significantly weaker, computing power was more limited, and much less was known than today about how best to apply either hardware or software resources to the problem of computer chess.
Part of the challenge was of course just crafting better engines, regardless of hardware, but doing so in ways that took appropriate advantage of whatever particular hardware one could get a hold of was a significant part of the problem as well. Also (and this isn't a trivial point), these competitions in earlier days were as much (if perhaps not more) a way for hardware folks to show off as it was for engine developers. Consider two-time world champion Cray Blitz (1983, 1986). Its success wasn't just a feather in the cap of Bob Hyatt et al. for their ability to design a strong engine, but also a source of advertising for Cray Research's supercomputer and its ability to outstrip others at handling the calculating complexities of chess.
While I'm at it, for a more obvious example of how hardware was long just as prominent and distinguishing a part of the equation in computer chess, we can think back to Kasparov's 1996-7 matches against Deep(er) Blue, which wouldn't have happened at all (think sponsorship and such) if IBM wasn't eager to test and show off its hardware.
All that said, there is currently a well-known competition that offers what you want to see, which is a hardware-neutral comparison that's specifically designed to determine the strongest engine: Martin Thoresen's TCEC, which e.g. ChessBomb broadcasts when it gets played.