There actually are horizontal relief forces, albeit transiently. There is a horizontal reaction force in the PSV in the transient case. However, both API and ASME (at least, for these diagrams) make sweeping assumptions they don't share.
a) pipe does not change fluid flow properties - i.e. infinitely short.
b) pipe only redirects flow.
c) relief conditions at the relief orifice are perfectly expanded outwards to discharge piping conditions - i.e. worst case, with previous assumptions considered.
However, for the case of open discharge relief systems like so, with very short runs of pipe (or even just the length of the bend), horizontal transient loads are very, very, very low.
My experience is that if a given length of pipe is shorter than the speed of sound divided by 1000 Hz, transient effects rarely have impact on SCH 40 piping.