This is because the tire.001 material is using displacement (directly from an image/color).
In newer blender versions this needs to go through the (new) dedicated Displacement node.

This is usually inserted for you automatically, the cycles addon runs a bit of code when it sees an older file

if bpy.data.version <= (2, 79, 1) or (bpy.data.version >= (2, 80, 0) and bpy.data.version <= (2, 80, 3)):
    displacement_nodes_insert()

This runs after the normal blender do_versions

bpy.app.handlers.version_update.append(version_update.do_versions)

Not exactly sure why this has not happened in your case (it is not clear what you exactly did when you say "imported into 2.8"... appended? opened the file?).
@Brecht Van Lommel (brecht): do bpy.app.handlers.version_update also run when appending?

I remember a similar issue in T54504 (where this apparently does not run when linking...)

@david (dasmitty101): That all being said, you can easily get around it by manually inserting the Displacement node (that takes the image as input and then goes to the Material Displacement input socket...)

Leaving this open for the time being (so we can get the question answered whether or not the cycles addon do_versions can be improved upon...)