The difference in power output (e.g. threshold power) between peak form and "off season" for most racing cyclists that don't stop training for any great length of time is ~10%, and a peaking period/taper will at most improve power by only a couple of percent, so we are not talking about huge swings in physiological capability. However winning margins in cycling are often only fractions of a percent, so even the marginal differences matter.
Also, because of the nature of the power-duration curve (i.e. it's pretty flat), a small improvement in aerobic power capability translates to a substantially larger endurance capacity. e.g. improving threshold power by 5% might increase the duration you could sustain your previous power level by 50%. That matters for long hill climbs where riders are trying to maintain the pace for as long as possible. If you are at the pointy end of GC, and only need to maintain a pace slightly under your own threshold (e.g. defending your place), your time to exhaustion will be much longer than others. So a peak that lifts sustainable aerobic capacities even a little can have a significant impact on outcomes.
In other sports there will be a differing mix of attributes required for success. Obviously fitness and physiological capabilities are very important, but skills play a much greater role in success in sports like tennis and football. Not all that much skill in a long hill climb where W/kg is by far the dominant success factor, compared with say being able to nail an ace to save a match point.
Nevertheless, players do still experience physiological peaks and troughs if they don't carefully manage their workload. Indeed team sports are only now beginning to use analytical methods for training load management that have been the domain of cycling (at least those that are in the know via power meter data) for well over a decade. Having said that, a large proportion of pro teams/riders were late to the party than many amateurs. Many pros are good despite their training.