Don't recognise it, though it's a common Horizontal Engine layout in full-size and models. I guess it's commercial rather than home made or a kit build. (A superior toy, better than Mamod, but not an Exhibition piece!)
There may be something missing, or incorrectly assembled, The piston rod and crank end coupling should be constrained by the cross-slide rails, marked in GREEN:
The piston bearing highlighted in RED wears badly ff the coupling is allowed to flex as the engine runs. Possibly your coupling is guided underneath and the top-view picture hides it?
This rough-finished Pottymill engine shows the coupling sliding on pads between four cross-slide rails:
Dave