Even in good condition (new) the Alfa gearbox mount seems quite 'floppy'. Those rubber washers can be replaced with a polyurethane type. Perhaps that'd minimize the side to side movement. Maybe the ones in your Spider are too thin?
There is a designed in side to side movement to allow the engine to move slightly on its mounts to overcome normal 4 cylinder engine vibration. The large rubber or poly washers are correct as is the additional clearance in this area.
It reassuring that some sideways play is normal. It isn't excessive and the rubber washers don't seem too bad. However I do have an old invoice passed on from the PO which includes a "temp repair to rear g/box mount" so I'll keep an eye on it.
The usual failure is either a sagging or decomposing silent block mount at the trans rear. There are temporary fixes, not worth the cost or effort as replacement of the silent block is a CURE. At the time, I will replace the rubber or poly washers if they show signs of deterioration. A rear sagging mount can cause all manner of symptoms, from popping out of gear, to exploding plastic fans into radiator and hood. This, with engine mounts is a good preventative maintence replacement item. It is also a DIY, and not terribly expensive. Those that replace sagging mounts are always suprised with the result.