documentation on display: -webkit-inline-box;
I'm thinking that it's old inherited code from flexbox.
You're correct.
Flexible boxes, defined by display: box and display: inline-box respectively, were old incarnations of what are now known as flex containers (display: flex and display: inline-flex).
They are described in this version of the Flexbox spec, but it doesn't say anything about these two display values other than
In CSS, flexible boxes (often referred to only as boxes in this specification) may be created by setting the ‘display’ property. A block-level box can be specified with a value of ‘box’ and an inline box can be specified using a value of inline-box.
Everything else is described by the box-* properties in the rest of that document.
Implementations and production sites still exist that use the old flexbox code, but it goes without saying that you should never have to use them today. Focus on writing CSS according to the latest Flexbox spec, which enjoys reasonable support by modern browsers and is on track for standardization.