Parliamentary systems don’t imply proportional representation necessarily. Commonwealth nations like Canada and the UK use the Westminster system, and use a first past the post system derived from that tradition for example. It simply depends on the country and who decided on the details of the electoral system.

The biggest features of parliamentary systems are usually that the head of state and head of government are not the same person, in particular the head of government is usually the leader of the party with the most votes, and generally there is some procedure where the head of state confers power to the government via a confidence vote, with the head of state holding the power to trigger elections when the current government is not meeting its mandate or following a vote of non-confidence in parliament.