Is EMI/EMC still a big concern for a PC case?
First off PC's emit a large amount of EMI, even with the case properly grounded they can cause AM radio signals to be completely 'drowned out'. A PC has multiple clocks and DC DC converters with very large switching currents and emits radiation. If your a 'nice' person you'll use a properly grounded case that is made of metal or other shielding material.
If your selling PC's they should be FCC certified.
As far as building them yourself and as far the law is concerned is a grey area, technically a device sold in a residential area should have an FCC certification. But a computer you build yourself isn't sold as a complete unit and isn't subject to authorization by the FCC (which costs thousands of dollars). The FCC suggests that you use a well grounded case. If you did cause interference with someone else's radio bands, the FCC could order you to shut the device off or fix the problem.

A personal computer is a special type of digital device -- a computer
that is marketed for use in the home.  Computers that are marketed
through retail outlets or through mail order  catalogs,  and
advertised  to  the  general  public,  are  considered  to  be
personal computers. In order to prevent the radio noise generated by
the digital device from interfering with radio communications, digital
devices must be designed to contain the noise.  This is accomplished
by:  1) designing the digital circuitry in a manner that minimizes
radio noise emissions; 2) enclosing the circuitry in a well-grounded
case that prevents radio noise from escaping; and, 3) including a
well-filtered power supply that keeps the radio noise from leaking
onto the electrical power lines.

Source: UNDERSTANDING THE FCC REGULATIONSFOR COMPUTERS AND OTHER DIGITAL DEVICES Page 2

What happens if a digital device causes interference?
Digital devices that comply with the FCC technical standards and have
been certified and marketed in accordance with the FCC rules may not
cause interference and must accept  any  interference  that  they
receive.    This  means  that  the  user  of  a  personal computer  may
be  required  to  shut  the  computer  off  if  it  is  found  to  be
causing interference to any authorized radio communications, such as
police, fire, TV or radio,even if the computer has been certified and
has an FCC ID tag on it to prove it.  In the event that this happens,
the user will be allowed to resume use of the computer only after the
cause of the interference problem has been eliminated.

Source: UNDERSTANDING THE FCC REGULATIONSFOR COMPUTERS AND OTHER DIGITAL DEVICES Page 14