Technically that is the wrong switch for what its doing. That switch is designed to isolate both the incoming live and neutral. However i can see it has been jerry rigged per se as the incoming live and neutral at the top has been bridged to serve another purpose. You are going to have an issue with it. Are you able to indicate which of those cables goes where?
To make the switch work, you'll simply attach the two wires you removed from the dimmer to the new switch. If there wasn't a grounding conductor attached to the dimmer, you have a couple options for grounding the new switch.
Add a grounding conductor
You can use a length of bare copper or green insulated wire, and connect it in an approved manner to the other grounding conductors in the box. Then you'll attach the other end of your grounding pigtail to the switch. You could use a twist-on connector, crimp connector, terminal block, push-in connector, or any other UL listed product designed for this.
Adding a grounding conductor is the preferred method.
Self grounding device
If it's a metal box, you could use a self grounding device. The switch will then be grounded to the box through the attachment screw, assuming of course that the box itself is grounded (which it should be if it's metal, but don't make assumptions when working with electricity). Self grounding devices will be labeled as such, and will have a little copper doohickey around the attachment screw hole.
NOTE:
If you're attaching a grounding pigtail to the other grounding conductors in the box, make sure all the existing grounding conductors stay connected. DO NOT permanently remove grounding conductors from the bundle, they must all be connected together.
Best Answer
A given switch has a specified limit on the total power it can control. Add up the total wattage of all the bulbs and if this is less than the limit for that dimmer, then it should work. Note that for LEDs you use the actual wattage not the equivalent wattage for an incandescent which gives the same illuminance (lumens).
Also the dimmer switch must be one which is designed to control LEDs. A dimmer switch from decades ago probably won't work. For years I used a 30 year old programmable dimmer which was approved for incandescent bulbs to control an LED by using one incandescent and one LED in the two bulb fixture.