text: New Beauty | Snowblower Forum
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  https://www.manualslib.com/manual/156947/Snapper-1030.html?page=8#manual
  Actually, sounds normal to me since it only does this when he pushes on it by hand - not when running. The horizontal shaft through the gearbox that attaches to the augurs is keyed to the driven gear in the gearbox to transfer torque, but basically the gear floats on the shaft, and lube is retained via the seals riding on whatever part of the shaft they contact. This is to prevent side loads on the gears due to bucket flex, bends, etc. and as long as it is not moving around with the augur running, seems normal to me, but could be aggravated by an impeller rear bearing that is allowing the box and impeller shaft to move (as I read your note, the augur proper is staging in place . . .).
  The gearbox on my Toro 521 does the same thing and has never been a problem-I wouldn't worry about it.
  The best snowblower I've ever used was a late 70's Snapper 826 with the short metal shute and a Briggs engine.I've been trying to get my hands on one for years but they are rare in my neck of the woods.
  Yeah, my experience on the Toros is like Mike C says, there is some slack in the side to side mechanism. What tadawson said for the reason makes sense.