Nitter does load videos but you may need to find an instance that's close to you. Once you do though it works better than Twitter's garbage ass video player. Check here and pick an instance with good uptime, try it and see how well videos load. Repeat until you find a good one.

Another benefit is when something is reported for "adult content" (as war videos often are), Nitter will still show them whilst Twitter will hide them unless you have an account.