Am I making any mistake because I was unable to access the exchange. I first tried it on my phone and then also tried it on my laptop.
If I want to access the site using zeusmex.com, this is what I will first see:.....
.....This makes it impossible for me to access the exchange.
Well, as you can see, Zeusmex has already announced that their service is under maintenance. They are working on rebranding the website and fixing some possible issues. I don't know how you were able to access the first page which you shared, but the maintenance is not finished yet and it's not only for you but for everyone else. You can see their announcement which I quoted below.
At the moment, our service is undergoing technical maintenance. All obligations to our clients were fulfilled before starting the maintenance. We apologize for any inconvenience caused. We will keep you informed about future updates.