This is not the case and you are missing something important. They are describing two patterns here.
The definition of gentrification I have been using incorporates displacement. It is essential to it, because the displacement is fundamentally the problem. The one they are using is not incorporating displacement as a necessity. Without the displacement, I would use a different term. So what would make these a "gentrification without displacement" different than a "gentrification with displacement."? A lack of demand pressure.
If you are looking at gentrification solely through a racial lens, there's a type that induces displacement, and a type that doesn't. The type that does will involve a housing shortage that is going to sharply raise rents from increased demand meeting a lack of supply. This forcibly pushes incoming and existing people down the socioeconomic ladder. This is very much the primary factor at play in a place like Minneapolis where you can see the housing supply vanishing at the same time rents are skyrocketing across the city.
The type that doesn't is going to likely be less due to economic pressure and more due to our national de-leading crashing the crime rate and making neighborhoods on the margin more appealing to people moving in or around the region. If there is adequate housing stock in the region, this is unlikely to be displacing people in the short or medium term because people in upper-income areas feel no pressure to move to lower income ones. It will alter the composition of the neighborhoods, and likely improve their socioeconomic status over time (which could cause issues in the long run as small incremental improvements occur) but the people moving in are not directly displacing the existing residents.
Actually, definitionally, the scholars have it right:
gen·tri·fi·ca·tion
/ˌjentrəfəˈkāSH(ə)n/
noun
- the process of renovating and improving a house or district so that it conforms to middle-class taste.
"an area undergoing rapid gentrification"- the process of making a person or activity more refined or polite.
"soccer has undergone gentrification"
- the process of making a person or activity more refined or polite.
Displacement is not inherent in the definition of gentrification; the definition of gentrification only really covers the literal transformation of values/qualities of the neighborhood/region. Of course, displacement is almost always a result of such a transformation, but not always; some incumbent residents resist displacement by eating the price hikes and acclimating to the change if they can afford it, though these people are obviously in the minority.
As for the 'housing shortage', that is also an effect; a result of urban development intentionally attracting affluent people to confined geographical spaces that cater to those gentrifiers' 'tastes' to the point where housing supply that can accommodate existing residents and the new potential residents is non-existent. Out of all of the housing available in a society, it's not a randomly distributed coincidence that upper class people tend to migrate to regions of upper class interest that are in short supply; demand for affluent urban homes didn't emerge out of a vacuum, so logically, it cannot be considered a fundamental cause of gentrification. Looking at the reasons for the demand to gentrify a neighborhood will get us closer to understanding the causes of gentrification than starting at the point where the demand has already arisen and isn't sufficiently supplied.