An extender may or may not help much. The extender will add significant latency that is "death" to gaming. A "long range router" is a marketing term that simply lets the consumer make the assumption that it differs from other routers. It isn't.
The best thing would be to run ethernet to the location. It may be more feasible than you think if done by a pro installer. It can also be done by anyone with the purchase of a few tools and without special training beyond Youtube.
The second place option is powerline networking kit. (The kit has the two needed adapters.) For best results use the Homeplug AV2 standard. These have the best service across a whole house. For lower cost, try any one you can afford to see if it works. Powerline is hit or miss, so buy for a customer friendly seller with a good return policy. Do this when you have a free day to install and the manufacturer's tech support is available.