No, the rules explicitly state what pieces are required from an earlier set:
This game is an expansion and requires that you use the following game
parts from one of the previous versions of Ticket to Ride:
A reserve of 45 Trains per player and matching Scoring Markers taken
from any of the following:
- Ticket to Ride / Ticket to Ride Europe
110 Train Car Cards taken from:
- Ticket to Ride / Ticket to Ride Europe / USA 1910 expansion
Anything not mentioned in the above list should be considered surplus to official requirements. Though you could always try playing with stations as an interesting variant!
EDIT: yes, without stations Heart of Africa is a very claustrophobic Ticket to Ride game. But this does seem to have been the intention of the designers, as they've admitted as much in a footnote in the rules booklet:
In 5 player games, the Heart of Africa (center of the map) area can
get crowded very quickly. Players beware! - and if you like your games
to be less competitive, stick with 4 players or less.