If there are rarely benefits how can the economy be reliant on it?
In terms of how the wealth flows into the economy in the first place, it's tech worker wages, which are of course taxed at a rate that would give corporations an apoplectic fit. The money that funds said corporations' needs in public infrastructure and educated workforce has got to be procured somewhere.
And if you're using that to, say, avoid raising taxes to cover things like inflation or new projects, over time, the level of pain you're going to experience when you either have to make all those adjustments at once or, worse, if the income source is removed, gets worse and worse.
edit: in this case, specifically, it seems like the concern is that even the limited amounts of income from tech companies and knock-on effects from their employees is an enormous lifeline to Ireland's economy, and they're afraid of the rebound effects if it goes away.