The page you've cited isn't wrong, but it isn't complete either.
Cooper enjoyed dinner at Audrey's house, agreeing to a large slice of cherry pie even though he was full to the point of bursting.
As I parse this sentence, the participial phrase is a supplemental modifier. It doesn't sensibly attach to Audrey's house, but it does sensibly attach to Cooper and to his enjoyment.
Mariah risked petting the pit bull wagging its stub tail.
In this sentence, the participial phrase is a restrictive modifier. Without it, we don't know which pit bull counts as the pit bull. Restrictive modifiers shouldn't have commas.
In 1879, a German engineer, Carl Benz, developed the first internal combistion engine, burning fuel like oil and petrol to power pistons.
As I parse it, this participial phrase isn't supplemental and it isn't restrictive. This is just a non-restrictive modifier. We don't need the information in that phrase to know what counts as the first internal combustion engine. Just "first internal combustion" is enough to identify which engine is the engine.
In this example, the participial phrase doesn't give us any new information. It's a restatement. "Internal combustion" means burning fuel like oil and petrol to power pistons. Many non-restrictive modifiers do give us new information, but information that isn't needed to identify the referent of the noun phrase.
Tᴚoɯɐuo, seeing things differently, presents a different answer.
The distinction between supplemental and restrictive isn't always clear. You and I have parsed "burning fuel like oil and petrol to power pistons" as a modifier of "the first internal combustion engine". Tᴚoɯɐuo has parsed it as supplemental modifier attached to the entire clause, acting as a description of Carl Benz's development. Both parsings are possible. Both parsings are sensible. Both parsings justify this use of the comma.
The phrase "seeing things differently" does count as new information in the example above, but we can identify who Tᴚoɯɐuo is without it.