Almost everything blocks electromagnetic radiation to some extent. Water and living tissue are good at it. Cacti do, but so do other plants; metal; plastic; clothes and water. Some of these are much better absorbers than plant tissue. There appears to be no evidence that cacti are better than other plants, for a given plant size. However thicker barriers absorb more than thinner; so cacti, being unusually thick plants, are probably slightly better than other plants (but worse than many other things). However even if this is true it is irrelevant because...
Electromagnetic radiation travels only in straight lines. So any kind of radiation shield works only if it is sitting between you and the source of radiation. So even if it were good at absorbing radiation, for a cactus to be effective as a radiation shield it has to be large enough to fill the space between you and the monitor, an approach which would obviously make the monitor unusable. Having a small cactus sitting beside the monitor will do nothing.
In short: this is a complete fabrication, supported by a few misleading half-truths.
The only way a cactus will shield you from radiation is if you have a giant one between you and your monitor. Even then its effectiveness is doubtful.