I can confirm that GZDoom requires a 32 bit OpenGL framebuffer, may be 0.9 versions worked in 16 bit modes but i doubt it. I think requiring 32 bit GL 1.1 is pretty much the same as requiring GL 1.2.
I've recently purchased for 10€ a laptop (hp omnibook xe3) with a s3 savage ix with 4 mb (based on savage 3d). It's the same only 16 bit GL 1.1 support. GL Quake (Fitzquake) worked but not GZDoom.
However i've tried again GLDirect 5.0.2 (from vogonsdrivers) and it works. There are some graphic problems tough. So it will almost surely work with the i815 as well. You'll want to disable CAD precision, i got a crash on exit (one of those in the 16 bit subsystem with a win 3.x type dialog) and then windows died. BTW quake was as disaster with gldirect.
With the trident blade xp it worked better than before with other GZDoom versions, also some graphic problems. There were more artifacts in the classic version with the trident driver than with the wrapper.
BTW i've added a couple of new low detail modes (3x2 and 4x4 not in release yet). They are a bit hacky tough since some adjustments were required.
Edit: i was wrong and in compatibility mode GZDoom is actually running in 16 bit mode. Seems like it's trying to use the microsoft software renderer and it won't run with the s3 driver even when allowing software. I've tried the promising 0.9.22 but it's the same, only works with gldirect.
Still crashes without the cad precision (LE version) on the s3 but not on the trident.