Update:
I just did not properly tested it - it is still the same - the table is gone, after I put there Responsive JEM into the template folder. Without it, it looks great, with the R JEM it is the same as before.
I tried another template and it works, so now I have this template (beez5) set as template for JEM pages and the rest of the site is on allrounder. It is not big problem, the JEM is for our club use only, so it is ok, but will be better with the same template...