Forklifts don't do much "hard" work. They just go back and forth, more than half the time with no load, and they use a hydraulic pump to lift. They do run a very long time, but again, not much load on them.
As I've mentioned many times, my late 70s IH2500b was a 50PTO HP gas engined tractor loader. It was also HST. Full cab, loaded tires, etc... about 8000#. It was also available with a diesel engine. Here's the specs for both engines below. As you can see, the diesel is larger and it has a more HP. Really, if you build a large displacement gas engine designed to do the work intended, you'd have to build a larger diesel engine to do the same work. It will cost a lot more, too. However, the diesel will be able to hold in the the torque curve longer, last a lot longer and use considerably less fuel. In and HST application like mine, it was recommended to run the thing at PTO rpms constantly. The diesel was much more fuel efficient and from talking to the guys at the industrial repair place I used a few times, the diesel was allegedly going twice as many hours as the gas before rebuilds under normal use. This was a late 70's design.
With that said, I had no issues with power and the gas engine. In a modern HST CUT or SCUT designed for mostly non-earth engaging tasks ( dirt plowing fields and pulling stumps), I'd have no issues with a gas engine. Its just turning a pump. You have to wonder why they stopped putting gas engines in them, then. It's probably because the diesel works better, lasts longer, is easier to work on at the shop, less parts to stock, and the manufacturer can charge more and make more profit.
Engine Detail:
International Harvester D-239
diesel
4-cylinder
liquid-cooled
239 ci [3.9 L]
Power: 67 hp [50.0 kW] (gear)
80 hp [59.7 kW] (hydro)
Compression: 16:1
Rated RPM: 2200 (gear)
2400 (hydro)
Oil capacity: 10 qts [9.5 L]
Coolant capacity: 14 qts [13.2 L]
Engine Detail:
International Harvester C-200
gasoline
4-cylinder
liquid-cooled
200 ci [3.3 L]
Power: 66 hp [49.2 kW] (gear)
74 hp [55.2 kW] (hydro)
Compression: 7.3:1
Rated RPM: 2200 (gear)
2400 (hydro)
Oil capacity: 7 qts [6.6 L]
Coolant capacity: 12 qts [11.4 L]