Short answer: no.
Tickera is perfectly capable of handling ticket sales by itself using one or more payment gateways integrated to it. Complete list of Tickera supported payment gateways can be found here.
So, why is WooCommerce then mentioned on this website so often?
Well, Tickera has seamless integration with WooCommerce via our Bridge for WooCommerce which, essentially, allows you to create and sell Tickera tickets like any other WooCommerce product. This opens up a whole new world of possibilities some of which are obvious (using WooCommerce payment gateways, creating ticket types as variable WooCommerce products, etc.). However, being number one e-commerce platform for WordPress, there is seemingly endless count of both official and unofficial add-ons for WooCommerce that grows daily. A lot of these can directly affect the way you sell tickets using Tickera, Bridge for WooCommerce and WooCommerce itself. To get the idea about what is possible we suggest you to read our posts here and here.
To wrap it up: if you want simple event ticketing system and are starting fresh with ticket sales, then it is perfectly normal and expected that you will be using Tickera as standalone (meaning: without WooCommerce). However, if you are already running WooCommerce on your website and have it all set up with your preferred payment gateway and shop page for selling other stuff, then it is only logical that you will be installing Tickera and Bridge for WooCommerce to sell tickets as WooCommerce products.