What version of DX a game uses and what version of DX you have installed are different things. It can be also said something similar with the driver/hardware -- you can go as high as you want with DX support, and be limited by your chip/driver when it comes to hardware supported acceleration. Your graphics chip & windows driver probably does have some kind of DirectDraw support, as evidenced by your test. You might be able to confirm more with dxdiag. But DirectDraw goes all the way up to DX 7, so you might as well run at least that, so you can try a DX 7 game if you want.
Every DX program, if you don't have hardware support for a feature, can fall back on a software rendering path. You might be able to run early Direct3D games, slowly, and run any Direct3D demo or game in full software too. So you can install any DX as high as you can go. The game won't use higher than it was programmed for.
The lack of framebuffer memory will pose some limitation to DirectDraw games, regardless of DX version. So you are looking at DirectDraw games, or really really simple early Direct3D game support on your PC, with any DX you chose to install. So what you will need will just depend on the game and if you meet the game's requirements.