Metastasis is the spreading of cancerous cells to a new site within the body where they form a secondary tumour. There is nothing special about how these metastases cause death, they do so in the same ways as the primary cancer eventually might:
- Replacing functional cells with non-functional cancerous cells
- Eroding into other tissues and disrupting normal body architecture
- Causing haemorrhage
- Putting pressure onto other structures
If we apply those principles to lung and liver secondary tumours, it is easy to see why they are likely to contribute significantly to mortality.
Cancerous masses in the lungs reduce the surface area available for gas exchange, reducing oxygen saturation of the patient. The tumour may also erode into a primary bronchus, which if obstructed would cause lung collapse, or into the mediastinum. If the mediastinum is involved then the great vessels or heart may be invaded into with significant consequences.
Liver metastases are more likely to cause problems due to the reduction of liver function as the cancer grows. This causes a plethora of problems as the liver is involved in so many pathways within the body. Examples of serious effects would include the patient becoming coagulopathic due to a reduction in production of clotting factors, making bleeding much more severe. The liver can begin to fail to clear toxins from the blood, leading to the risk of acidosis or hepatic encephalopathy (leading to coma and eventual death). If the tumour were to invade the portal vein, this can cause portal hypertension, which in turn shunts pressure into the systemic venous system. This can cause oesophageal varices which are prone to spontaneous and catastrophic bleeding. Similarly a tumour invading the common bile duct (or other part of the biliary tree) can cause obstructive jaundice and associated problems.
The reason your quote suggests that most deaths are from metastases than the primary tumour is probably because tumours in these locations have greater negative effects at a smaller size because they are in crucial tissues.
There may be another contributing factor in the form of data interpretation, however. Tumours are often 'staged' via the TNM staging system, the last component of which is the presence of metastases. The presence of distal metastases automatically makes colorectal cancer Stage 4. This is often considered not to be curable, meaning a move to more palliative treatment options. This may affect the survival curves for those with distal metastases and those without.