It is pretty much the same game as in the "Multiplayer tutorial 4: real-time game" by Ashley except this one also syncs a bullet projectile. Testing the game even in localhost (with 2 browser windows) has some slightly but very noticeable and annoying input delay.
What can I be doing wrong?
You probably aren't doing anything wrong. By default the multiplayer plugin is using "Internet" as the bandwidth profile, which adds some delay in order to compensate for high latency and high packet-loss connections. I highly recommend to read the manual before doing this but if the connection is stable enough (e.g. regional), switch the bandwidth profile to "Lan" by using set bandwidth profile.
I've personally added an option for users to switch the profile by themselves but basically the worst things that can happen (based on my experiences so far) are rubberbanding or peers getting timed out because they couldn't keep up with the faster rates that the "Lan" bandwidth profile uses.
I'd personally really like to see an update to make this feature of the multiplayer plugin more adaptive and based on the connection quality of all individuals in a room, instead of using fixed values.