Can I use a ethernet splitter to connect a router to two devices? [duplicate]

No.

A star shared regular Ethernet network can not be split by just tying cable together. If you want to connect two devices simultaneously to the same cable then you ether need a hub or a switch.

The device you are showing in your post is either one of these two:

1. A physically wired 1:1 splitter which means that you need to switch off one of the devices connected to it while the other is connected.
2. Or a dual 100mbit Ethernet over a single 8 wire cable.

The explain these a bit more:
Plain old 10/100 Mbit Ethernet has a standard cable with 8 wires, 4 of which are used. If you creatively rewire a few of these and (un)rewire those at the other end you can use two fully independent connections of the single cable.

Note that this just act as two cables in a single cable package and that you still need something to get the devices to talk to each other.