A dual band WiFi would likely ease the gaming problem. Particularly if the Roku can use the 5GHz band and leave the 2.4 GHz free for less demanding tasks. Placement of the equipment can affect the usefulness of the current or a new router, so you should investigate getting the gaming and wifi source closer to each other. Dual band routers are becoming old technology as 802.11ad is emerging, so pretty good equipment is falling in price. There is no need to overspend to get a decent router.
Buy from a store with a customer friendly return policy and install the router right away just in case it doesn't help. It is certainly worth investigating better wifi before paying for a separate internet connection.