In this sentence it means space. The big trainer is too big. If it were a building part, then it would be best said 'my house doesn't have a room for the trainer.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
northwind #4. My house doesn't have a room for such a big trainer.I'd say, "My house doesn't have a room [which is] suitable for such a big trainer."
northwind #6. the empty room
#7. the little room
#8. the occupied room
#9. the open room
#10. the small room
#11. the tiny room
#12. the vacant room
#2. space for something.
#3. part of a building enclosed by walls, floor, and ceiling. All of these refer to #3 by specifically naming one particular enclosure within the house.