The processor is not so much an issue as it is the hardware archetecture. I'm sure sopwith could possibly run on a Tandy TRS-80 2000 or some other Semi-Compatibles if it was programmed "by the rules" well enough. The 80186 was also used in a few very early portables and laptops, as well as at least one IBM Compatible model by I think Zenith, or it might have been an Amstrad. All the 80186 is is an 8086 with a few extra instructions. There's also an 80188 as well, but I can't think of a compuer with one. Those two chips were more often used on expansion cards than on an actual motherboard as a CPU, and were not used post 1984 on any systems at all.
Sopwith runs too darn fast on just about anything long of a 6Mhz 80286. I ran it on a Compaq Deskpro 386/16 once, and it was still too fast. It runs best though on a 4.77 Mhz 8088 with CGA from my experience, which I'll have eventually (I just got the boards from Terry, just got to get the floppy booting more than Microsoft Adventure and an 8-bit IDE controller, and away we go).
As for other good old games to play.......these are some of my favs.....
Tank Wars
Leisure Suit Larry 3
Scorched Earth
Adventure
Lawn Mower Simulator
ML Yahtzee
I got some stuff I need to upload, some pretty cool old shareware and freeware, and BASIC games that I have not seen anywhere else, or that are very hard to find. Once I find a decent file host that allows direct linking, I'd love to post links on my site for them. I raided my sister's old collection of old software from the days when I was first getting into computers as a 10 year old reluctant gamer geek, when she had a 386 running DOS in college.