The problem with the bike in the second picture/link you provided is that the rear rack is attached to the frame on a suspension bike. Thus if you mount an engine on the rack, when the back wheel goes up and down with the suspension it will cause your drive chain to fall off.
If you/or the welder...................................
Could take the rear rack off/unweld it from the frame and use torsion bars or make a way to make it mount to the rear suspension arm it might be possible to still utilize this frame. Would it be too weak?........Lots of factors and variables are involved. One of them being.......
The size and weight of your powerplant(engine)
Do you have a pict. of the engine you are planning on using?