I mention the zoning thing only to explain why you can't push "just open a competitor" one level deeper and create your own vertically-integrated competitor - most regions have an essentially fixed number of major venues, so getting 100% buy-in is totally possible.
But yeah, it's not the proximate cause. That's just vertical control of the market, where TM took over online sales for people who needed a POS service for the web, then merged with LN to get control over promotion and venue operation (which among other things means that many box offices charge fees that get passed on to TM).