Arkcon, this technique is typically used to purify small amounts (tens of mL) of acrylic monomer immediately before use in a free radical or controlled radical polymerization (like ATRP). The inhibitor (almost certainly BHT or MEHQ) prevents autopolymerization during long storage. Methyl methacrylate, as well as most common monomers, is stable for weeks at room temperature on the bench without inhibitor.
When stored without inhibitor in large scales, autopolymerization can result in thermal runaway, which is why typically only small amounts are purified by neutral alumina plug or distillation. Another approach is just to add more radical initiator which will consume the inhibitor then begin the reaction, but this is not an optimal method.
I agree that calling this column chromatography is a misnomer, this is simply flashing monomer through a plug of alumina.
OP, to clear things up, this is how I would perform this very simple technique. Take a small fritted column, add a about 5 cm of neutral alumina to it, then pour your pure monomer on top. Add air pressure and collect the disinhibited monomer from the bottom. Thats all. Its not a real column. I've done this with cotton as a frit in a pasteur pipette before, its foolproof.