This is coming from the newest alpha build of Google Chrome, Canary, and also functions the same way on chromebooks (and has for the many months I have had it).
When I hit enter on my fightlist it fights the selected character but it also opens the drop down menu which requires me to hit enter again for it to close. In the end my lazy butt has to hit enter twice as many times in order to go through my fight list.
This is not reproduced if I manually click fight with the mouse. Just something to be aware of when Chrome eventually updates as then Chrome and Firefox will both have issues.
I am on build 31.0.1601.1