Your seedling is not dead; however, you removed the seed cap TOO EARLY and have exposed the tender underdeveloped cotyledon leaf. People will often get impatient with the germination process and want to take "helmets" off the second they see a sprout above ground. I've found that the fastest sprouts in a batch of like seeds will often wear a helmet. These are the seeds that sprout fast, sometimes weeks ahead of the average germination rate for a batch from the same pod. Rapid starts like these don't always end up culls; however, from a germination standpoint, they almost always exhibit lopsided growth. This is due largely inpart to phytohormone instruction and above average commitment of stored energy for root initiation vs. cotyledon leaf development. The testa (helmet) allows the first set of leaves to grow under ideal moisture conditions until they naturally unfurl from the protective case and begin the process of photosynthesis. Your seedling will die if cotyledon leaves are allowed to dry. Putting a dome over your seedling to replicate what nature intended for the testa, is advisable; however, you will need to monitor the jump in relative humidity. The problem then becomes balancing moisture levels needed for your cotyledon leaves to properly develop while keeping RH levels down around the stem of your seedling to defend against damping off (fungal infection and mold). If you decide to cover the seedling, I would offer the following suggestions.
Remove bottom heat.
The reccomended temperature range for germination of Capsicum is 70-85 F (James M. Stephens, professor, Horticultural Sciences Department, Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida). I find best results for germination when I use a source of bottom heat to bring the ambient temperature in my incubator to 80F. Once your seeds germinate, bottom heat is no longer necessary and can actually inhibit root development, potentially encourage root rot and lower the amount of available oxyegen in the root area of your seedling (see dissolved oxygen in water). A moist and warm environment is often the spark that initates seedling "damping off".
Suppression with Natural Fungicide
Mist the top of your growing media with Chamomile tea to supress fungal growth and then dust with cinnimon. This is a well tolerated treatment; however, avoid coating the tender stems of your seedlings.
Bottom watering
Pouring water over the soil is a great way to keep the surface of your growing media wet for fungi and mold growth. Water your seedling from the bottom to avoid this and reap the added benifit of greater root development.
I normally cull seedlings like yours to allow others a shot at the title; however, there are times when I let them go for it anyway. If they make progress, the cotyledon leaf unfurls slightly (still tiny) and begins to turn a pale yellow or green color. When the leaves (still small) turn green, it is poised for photosynthesis and may survive. Remove dome, place a little further from the light than other seedlings and make sure to provide breeze from a fan to increase respiration, strenghten stems and keep the surface of the grow media dry.
Best of luck
Matt