So that's not quite how ChIP-Seq (Chromatin ImmunoPrecipitation and Sequencing) works. First, you start out with a large number of cells per sample (preferably on the order of 107 or more - the more sample, the more immunoprecipitations you can do to different targets) and do whatever it is that you're going to do to induce transcription factor binding - expose cells to drugs, treat with cytokines, grow in different conditions, or simply compare two types of cell populations - normal vs. cancer, etc. After a certain period of time, determined by your experimental setup, you cross-link the cells with 1% formaldehyde, which fixes everything in place, including transcription factors bound to DNA. The cells are then broken apart by incubation in a detergent-containing buffer, and nuclei are harvested. After washing, the nuclei are either incubated with micrococcal nuclease (MNase) to digest DNA into strands of 1-5 nucleosomes in length (150-900 bp), or sheared by mechanical ultrasonication, hopefully leaving strands of the same length.
Once you have your DNA strands, you add antibodies to specific targets - either certain forms/post-translational modifications of the histone proteins that make up the nucleosome, or to specific transcription factors or TF families. The antibodies bind to their targets, and are enriched by incubating with (generally magnetic) beads that have the antibody-binding protein Protein G covalently attached to their surfaces. The beads are washed with low-salt and high-salt washes, then the formaldehyde cross-links are reversed and the chromatin is eluted from the beads in an elution buffer at high temperature (65°C) with vortexing in a thermomixer. Any remaining protein is removed by digesting with Proteinase K, the DNA is purified using a spin column, and you now have your enriched, purified DNA sample ready for sequencing.
Antibody binding and enrichment of known sequences is often first analyzed by regular PCR, just to ensure that everything worked. Once your sample has been validated, it is then prepared for next-gen sequencing. We are now near Step 1 of your illustration above. The read lengths of some instruments may be shorter than the average length of the fragments you prepared during the ChIP step (150-900 bp), so during the library construction phase they are further broken down into shorter strands before having the common primer templates ligated to them (if that's the technology you're using). Even if the instrument allows you to use the full length of your DNA strands, you need to remember that the sample is the aggregate DNA from millions of cells, and they didn't all break after MNase digestion in exactly the same way.
After amplification and reading, you are then left a large number of short sequences, which need to be compared to a reference genome and aligned:
Since we've already enriched for certain regions of DNA by using the antibodies which bind to DNA-bound or -associated proteins, there will be a larger number of similar overlapping reads in enriched areas, allowing us to tell where the histone, transcription factor, or other protein was bound when the sample was originally cross-linked.
Hopefully this all makes sense to you. I based my description of the ChIP protocol on Cell Signaling's SimpleChIP products, which I've found to be of quite good quality and reproducibility (no, I don't work for them!).