Every manual I've ever had loose has been like that, though in an ideal world it wouldn't be. In the diagram below, on the input shaft, surface (1) is supported by bearing (2) which is held at the front of the case. On the output shaft, surface (3) is supported by bearing (4) which engages in the back of the input shaft. Because of the connection between the input and output, any clearance between the bearing and surfaces results in movement, which you see at the front of the input shaft. Once the transmission is installed in the engine, the front tip of the input shaft (5) is engaged in the pilot bearing at the back of the crank, basically eliminating that slop, and stiffening up the assembly.
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