PSP-E1000 (Street) Has No Touchscreen

Correct. The PSP-E1000 "Street" (2011, budget model) does not have a touchscreen.

• Controls: Standard PSP layout: D-Pad, Face Buttons (△○×□), Analog "Nub", Shoulder (L/R), Start/Select, Home, Volume, Hold, Power.
• Removed vs 3000: No Wi-Fi (802.11b), No Mic, No Video Out (AV), Mono Speaker (vs Stereo), Matte finish, UMD drive manual latch.
• Screen: 4.3" 480x272 LCD (same res), non-touch.

Only the Nintendo DS/3DS, PS Vita, Wii U GamePad, Switch (and smartphones) have touchscreens in that handheld generation.