そうやって俺のことを気にしつつ、しかし素直になりきれない、そのツンデレさが今若い男の間で大ブーム！

、、！

So while you're doing that — thinking about me but not quite able to be honest about it — that tsundere-ness of yours is all the rage among young men right now!

Literal

So-doing me [gen-の] thing [obj-を] concern-[while-つつ], but honest become-[cannot-完全-きれない], that tsundere-ness [subj-が] now young men [gen-の] between [at-で] big-boom!

気にしつつ 'while concerning yourself about' uses the conjunction ~つつ, a more formal/literary sibling of ~ながら. なりきれない is the compound potential-negative 'cannot fully become' — using the ~きる 'fully' auxiliary in its negative. ツンデレ 'tsundere' is the famous anime/manga character archetype: aloof/prickly (ツンツン) on the surface but sweet (デレデレ) underneath. The suffix ~さ nominalizes it into 'tsundere-ness.' ブーム is the loan for a fad/boom/craze.