I just had an MRI: Right peritrigonal chronic leukomalacia with some gliosis and compensatory dilatation of right trigone. What does this mean and could it be causing dizziness and balance problems?

Abnormal MRI. Possibly--you should be seeking a Neurologist or Neurosurgeon's opinion.
Not likely. It looks like an old injury, possibly in childhood. The likelihood that it is causing symptoms is extremely remote. The MRI isn't the patient; you are. The proper person to address this with is the doc who ordered the MRI. The MRI by itself without clinical correlation is meaningless. Ask to see the images. In radiology, 1 picture is worth 1000 words.
Unlikely. The chronic nature of this suggests an older injury,and is not localized in an area that should affect your balance nor cause vertigo.