Can I pack a gas engine in my check-in luggage

Out of personal experience, there is no problem as long as it is new and it has no oils or some sort of residue that might leak.

I have put RC plane engines in checked luggage many times, some of them are more than a 100cc. One time we also put an RC jet engine in a checked luggage with no issues at all.

It's an engine not a motor

I know engine people use the terms interchangeably, but they're not. A motor is an electric motor - made out of copper, iron and insulating varnish, it contains nothing to endanger flight. So don't go by what the materials guidelines say about "motors".

Why does this matter? You may be shipping an engine, but other people ship electric motors. The regulations will be written for both people, and so the regs need to distinguish a motor from an engine, since they have different requirements.

Engine oil is no-go

At the least, you will need to check your engine for lubricating oils, which ARE flammable - extremely flammable if leaked and soaked into other people's clothing. Oil-soaked rags are every shopmaster's worst nightmare. Oil seals on an engine are not hermetic, and absolutely will leak if the engine is oriented the wrong way. (trust me, I once had an engine tilt about 40 degrees while being hauled, and I found the carburetor bowl full of engine oil! Whaaaa???)

The oil might be in the engine crankcase, or might be in a bottle in the packaging. In the latter case, follow the airline's instructions for shipping oil in a bottle. But I would simply leave the oil in the US, for climate change reasons alone - it will take several times the oil's weight in jet fuel to transport it, with CO2 release many times more than that! Someone in the US can use the oil productively... though I wouldn't put oil from Harbor Freight in any machine I care about, lol.

Why fly a cheap Chinese engine across an ocean?

Predator is a private-label brand of Harbor Freight, a retailer that's all about cheap tools. That's their fame and reputation. US buyers expect junk, and plan to run them til they fail, then throw them away and buy another (possibly a real Briggs & Stratton). There's no parts support. Harbor Freight relies on Americans not bothering to return faulty items (which is a pretty good business model, as it turns out).

Here's the nominally same engine at the HF site. Take a close look at the 2 engines. See how the markings are the same but the engine is different in many subtle ways? That's because this engine is a "private label" re-marking of whichever random Chinese-builder engine is cheapest for this supply contract.

Seriously. You will find higher quality engines at a junk shoppe or flea market.

So why not just do that?