A detector containing two radiopure 116CdWO4 crystal scintillators with total mass of 1.2 kg was operated during 35324 h at the Gran Sasso Underground Laboratory (INFN, Italy) with the main aim to investigate double beta decay of 116Cd. As a by-product of the experiment, a new upper limit on atomic abundance of hypothetical naturally occurring long-lived seaborgium (eka-tungsten, Z = 106) in tungsten was set at 5.1 ∙ 10-15 atom(Sg)/atom(W) with 90% C.L. (assuming the Sg half-life of 109 yr) by the analysis of the alpha decay events. This limit is better than those obtained with a ZnWO4 scintillator and in other types of experiments which used the accelerator mass spectrometry or searched for spontaneous fission of superheavy elements.